[Music] [Music] hi everyone my name is Ravi Prakash and this is the ninth class of geometry okay so from here onwards in each few videos we'll discuss about condition for formation of Crangle right so in how many conditions triangle can be formed triangles like optical triangle acute angle triangle scalene triangles like that okay right angle triangle so we'll discuss all these things okay see when those sides are given when those sides are given the third side when two sides are given third side should always be right this third side should always be less than some of the two sides and should always be greater than difference of two sides difference of two sides okay so when two sides are given third side should always be less than sum of two sides and all it should be written as sum of difference of two sides okay so that rivers always be know right from childhood will childhood which way we study it is sum of two sides is greater than the third side okay so this is the condition right for example if sides of a triangle are 7 to L and n right for how many for how many integral values of pen for how many integral values of n triangle will be formed Brandon will be formed right that means n should be always less than sum of two sides that is 7 plus 12 19 and n should always be greater than difference of two sides right it is 12 by 7 don't take sine minus 2 will read any this difference cannot be negative right so always positive 30 12 minus 7 so 5 is so that means n is between 5 and 19 right therefore and can take how many values so n is from five to nineteen so n can take any value from 6 to 18 how many values both inclusive right so in both inclusive difference plus 1 so 18 minus 6 12 12 plus 1 13 so 13 is the answer I'd so n can't take 13 values so if sites of a triangular 712 and n 4 how many integral values of n Taronga will be formed that is for 13 values of n right that is n is from 6 to 18 ok now next one if two sides of a triangle are two sides of a triangle are 7 62 and 12 33 units 12 33 units so for how many for how many integral values of third side for how many integral values of third side third side a triangle will be formed a triangle will be formed okay so I can directly write the third side BX the third side let the third side be X right so X should lie in between these two right sum of two sides that is 7 62 plus 12 33 difference of two sides side 12:33 minus 7 62 that means X is lying between what the summation of this 2,095 okay sorry 90 95 sorry 1995 right 1995 put a difference here 12:33 - 760 - right so it is 471 I think yeah 471 so 471 right so how many values here that means X can't take all the values from 472 to 1994 right so again both inclusive what is the what are the number of values difference plus 1 right that is X can take how many values 1994 - 472 the difference plus 1 because both inclusive 472 and 1994 both inclusive right so what is the difference here it is 1520 2 plus 1 1523 right 1526 down sir right so for how many general is of X for how many integral values of x or of third side what is answer as is 15 23 second forum 15 23 different angles okay this is the concept here fine now next one how to how to categorize for given size a triangle is an obtuse angle triangle or up to acute angle triangle right so see for any right angle triangle it is the condition for any right angle triangle or I should give in first give the heading s condition for Optus acute and right right angle triangle right note is obtuse angle triangle so obtuse angle triangle is a triangle in which one angle is greater than 90 degree this is obtuse angle angles acute angle angle is all angles are less than 90 degree right reading done you know one angle is equal to 90 degree right this is difference between acute obtuse and right angle triangle so now choose one angle is greater than 90 degree right to find the condition let's write it for a right angle triangle first to right angle angle right so I know right angle triangle to the condition for right angle triangle if it is a it is B so C square should be equal to a square plus B Square this is Pythagoras theorem okay so C square is equal to a square plus B Square now from here on we can derive a condition for this is for right angle triangle right this is for right angle triangle so we derive a condition for optimal triangle right rock pigeon little triangle what will happen this files this side will be more tilted right because angle has to be greater than 90 degree right angle has to be this angle this angle theta theta is obviously greater than 90 degree right this is for optimal triangle know we're discussing for octaves angle render now see what is the condition here when this theta was exactly when this theta was exactly equal to 90 then this C ladies side we see the side we ate this side will be right then is C is square was absolutely equal to a square plus B square right but when this theta when this theta is in green that is more than 90 degree this side will expand so at 90 degrees C square was equal to a square will be square right now if it is more than 90 this side will further spend right so now it will be like it will believe C square would be greater than a square plus B Square are you getting it I assume it to be a at assume this to be this triangle to be made of a stretchable wire right so it's a right angle triangle so right angle triangle this C square is absolutely equal to a square plus B Square Pythagoras theorem right now in case of obtuse angle triangle this set is tilted okay so this side is to you know this is a triangle right so this 90 degree expands so if it is a stretchable wire material this hypotenuse of right angle triangle will also expand right so if 90 degree opens up right it is Theta is more than 90 degree now to general triangle this potin is also expands right so when it was when it is 90 degree C square that is hypotenuse is equal to a square plus B Square when it is more than 90 degree it expands right well it disbands C square will be greater than a square is B Square right and obviously we know that in any triangle in any triangle larger the angle larger the angle longer is this side larger the angle longer is the side right obviously because more is the angle that it's larger the angle longer is the should write longer is its opposite side I could write like this longer is its opposite side right in any triangle if angle is more its opposite side Allah more expanded right so it's the full side anymore so if more is the theta it's a pulled side is more right say no presently triangle only one angle can be more than 90 degree right because some have to be less than sorry some have to be equal to 180 degree in any triangle rate so if one angle is more than 90 degree some of other to end this has to be less than 90 degree right so that means this this is the greatest handle this is the greatest time the rate this is a British triangle here that means C is the longest side C have to be the longest side right rewrite in words this one in obtuse angle triangle longest side square should be greater than sum of squares of other two sides other two sides right very important condition market in obtuse angle triangle longest side square is greater than sum of squares of other two sides okay very important condition right similarly we can discuss for acute angle triangle also right we can discuss for acute angle triangles all right here itself so that all will be in one screen okay in case of acute and then Randall now what if in case of acute angle bracket again sense if I know right and we can compare it by radical triangle reading with Rangel if theta is 90 degree so it is perfectly equal to AC square is equal to a squared a is capital B Square right now in this case theta will further contract this acute angle triangle it is Theta is now less than 90 degree this C squared no at 90 degree it was perfectly equal to a square plus B Square if theta expands this is more than 90 degree opposite side also expands that is an obtuse angle triangle the C square is greater than a square plus B square now for right angle triangle if theta contracts right that is two acute angle right angle is less than 90 degree so this side will for the applet safe theta perhaps a poet side will further contract right that means the opposite side will be what will be less than in this case less than a square plus B Square so this is the condition for acute angle triangle right this is a condition for acute angle triangle is for any side right because in this case all the angles are like less than negative only so all the angles are less than 80 degree only right so square so getting accurate angle triangle always C square will be less than a square plus B square always any side you take thread it will be less than this sum of squares of other two sides for sure so let's do some example you know we need to check here that okay 12 18 and 23 is which kind of Crandall acute obtuse or right angle triangle which kind of triangle right acute opt user right angle trundle now you can sense it reduces this is obviously not a right angle triangle this is obviously not a right angle triangle because it doesn't follow any Triplett it doesn't follow any Triplett so it is not a right angle triangle okay moreover moreover what you can do here is to find out of acute and obtuse acute and obtuse right so what you can do put the condition of obtuse right what is the pension condition for obtuse longest side square condition for obtuse law inside square should be greater than sum of squares sum of squares of other two sides right of other two sides fine okay that means for a long and shatter square at 23 square 23 square should be greater than 2 nu square plus 18 square let's check is it true 23 square is what 5 29 4 is 12 square 144 what is it in square 3 24 right so round 144 plus 320 force of 529 is greater than 468 right it is correct that means this triangle is an obtuse angle triangle this triangle is n of two's angle triangle it is not an acute angle triangle not a right and enter ended correct so this is how we check for any any progress right any triangle you check like this red suppose entry I need to check let's say 5 512 ok 512 and 7 ah which kind of triangle a cute of tubes or right angle triangle so again you can see that it is not in right angle triangle because it doesn't follow any turbidity right so for a cube optimal triangle again condition longest side is square foot D condition for obtuse angle triangle longest side is square to every square should be greater than v square plus sorry 7 square yeah that means 144 should be greater than 7 is square plus v square so 49 plus 20 or 74 credit only right that mean it is an obtuse and you time didn't always right it doesn't always obviously ok but right now it is obtuse angle triangle now let's change your suppose I change it I make here 5 12 and 14 you know right or I get I can make here if I know that 5 12 and 13 will give me writing a triangle 512 it is a triplet here right five two threes interpretive okay now let let me make the side says 5 11 and 12 5 11 and 12 now is it acute or obtuse obviously obviously it is not right angle triangle so it is acute or obtuse can we check we can check quickly it takes the cultural condition of design your dragon you can put four cute also right then just putting four up to it is easy to put five square is 25 plus 11 is square right long gate side square should be greater than sum of the squares of other two sides fine 144 is greater than 25 plus 121 that is 146 it is wrong it is wrong that means it is what it is in a cute angle right it is not it is not an obtuse angle triangle it is an acute angle triangle so this is how we check for acute angle triangle an obtuse angle triangle right I hope you got it okay let's do some questions now fine okay question if two sides of a triangle are 8 and 15 then for how many then for how many integral values of third side then for how many integral values of third side triangle will be an obtuse angle triangle obtuse angle triangle and this is previous air cat question right so just give it a try ok pause this video for two minutes or at least 5 minutes and give it a try you can solve it right ok we will solve No so if two sides of a triangle er 8 and 15 then for how many integral values of third side triangle will be an obtuse angle triangle fine ok that means let's cite lady sides B 815 and X X's is a third side right so X will lie in between sum of two sides is 23 and difference of two 37 right that means X can take all values from 8 to 22 that means it can take X can take 15 values no but this is what this is for all kind of triangles form bride obtuse acute right angle triangle whatever all the mixture there are total 15 values so I get form fifteen different angles right but our question is for obtuse angle triangle right so for obtuse angle triangle n what is the condition longest side square is greater than sum of squares of other two sides right but if you see here X can take the value from 8 to 22 okay and the one side of triangle is about 15 that means X is sometime less less than 15 and X is sometimes written as greater than 15 right so there will be a kind of controversy if I directly pick any value for X right that means it is kind of for two cases we are seeing that two cases can be formed right what is the first case first case where if X is less than 15 then this if X is less than 15 then this 15 becomes the longest side okay and if X is greater than 15 because X can take all values from 8 to 22 right 15 will lie somewhere in the middle right if X is greater than 15 in that case X is along each side right so I can make two cases here okay let's make case 1 case 1 if X is less than 15 then 15 is the longest side 15 is the longest side in that case 15 squared at a longish ID square should be greater than sum of squares of other two sides that is X square plus KT square okay so what is the answer in this case or again red or 15 squared is 225 minus 64 or X square is what it should be less than 225 is 15 square minus 8 squared is 64 so 225 minus 64 becomes 161 X square is less than 151 that means X can take all the values from X can take on Z values that is less than equal to 12 right because x squared is 161 so 13 squared is 169 so X can't take 13 so X will start taking from 12 because X is 13.7 sorry 12 point something right so large integer X can take it 12 so X is less than equal 12 but where till 8 because before 8 triangle will not reform forget about up to the new triangle only triangle cannot be formed right because what is the first condition for formation of triangle X should be between 8 and 22 that means X is less than 12 right therefore X can take 5 values that is X is equal to 12 11 10 9 8 right so here X can take 5 values here X can take 5 values right now cage to cage to cage to if X is greater than 15 then X is the longest side now because the two other sides are about 8 and 15 so if X is greater than 15 so X is the longest side so if X is along each side X square is greater than 80 square plus 15 square that means X square is greater than 289 that means X square is what greater than what is 289 7 a square that means X square is greater than 17 square right that means X has to be greater than or equal to 18 or X has to be again right greater than 17 can read/write so X has to be greater than 17 that means X can't take 17 X will start taking value from 18 says can take 18 19 20 up to where up to 22 this is a maximum limit right 20 21 22 so again X can take 5 value 0 so again X can take 5 values in case 2 also what is the answer 5 + 5 what is answer 10 so answer is 10 therefore n is the answer answer is 10 so for how many integral values a value value the third side dragon will be up to then you drag in 10 values correct okay now in the same question you can ask okay from 8 obviously so from in the same question I can write it okay that okay X could take values from 23 to 7 right so X will be from 8 to 22 fine is can take 15 values okay now I got okay out of this 15 values I got the we obtuse angle triangle bill 10 0 10 obtuse angle triangle right so can you find number of acute angle triangle as well as right angle triangle how many last question how many up to Zenit angle you got 10 right how many acute angle triangle how many writings will crank then to see since 8 and 15 are the other two sides so there's a triplet right here if you remember 815 70 is a triplet or you can satisfy the parrot prices are also right at 815 so 815 70 is a triplet that means there is only 0 only be one right angle triangle then only will be one right angle triangle right so there can be 15 distinct angles can be found out of that 10 is obtuse one is acute sorry one is reading it wrong is how many acute 15 minus 10 plus one that is how much four there are four acute angle triangles in obtuse angle triangle one right angle triangle right so good question it is fine okay okay next one we'll discuss this question yeah so the next question is if two sides of a triangle are 10 and 24 right 10 for how many integral values of the third side triangle will be an acute angle triangle right ok so again let's say the sides of triangle at 1024 and X right so it should be word should lie between some of two sides that is 34 difference of two sides that is 14 that means range of X is what from 14 to 30 for both X exclusive pride that means 15 to 33 okay so now X can't if X can take all the values from 15 to 33 again same thing as a last question right because 24 lies in between so if X is less than 24 then X is a larger side sorry than 24 the larger side and if X is greater than greater than 24 that means 24 is a sorry then X is a larger side right so if X is less than 24 that means 24 the larger side here given and if X is greater than 24 2010 and 24 so that means X will be the credit side so again two cases L mean so case 1 case 1 if X is greater than 24 then X is the law and larger side so X is the larger side so it notice for academic wrangle largest side that is X square at largest site it is X square should be less than sum of squares of the other two sides that is 10 square plus 24 square okay that basically means X square should be less than now 24 squared is 4 75 76 and plus 10 square is 676 so X square is less than 676 and 676 is 126 square that means X square is less than that means X square is less than 26 square therefore X is less than 26 the first condition I got X is less than 26 right now case 2 case 2 if X is less than 24 then 24 is the larger side 24 is the larger side ok that means X largest red square 24 square should be less than X square plus n square that means X square should be greater than 576 minus 100 that is 476 this is roughly around how much rate C 22 square is 484 right that means X square X is greater than 21 point something right that means I can say that okay X can be greater than equal to 22 right because x squared is greater than 476 what is 476 21 point something sorry but it means the square root of 4 addresses what 21 points something right that means X can take the value from 2002 onwards right so 22 onwards this is a second equation but only less than 26 that means X can take how many values therefore X can take how many values X can take 22 23 24 and 25 that's it press on set answer is 4 so 4 is the answer for this question right so it's a very good question and is a very good concepts right so the next video will discuss if perimeter is given right so how to find number of triangles in scalene triangles or skyrim triangular hama dragons can be found when parameter outside is given that means sum of all three sides is given right okay thank you [Music]