Question

the lengths of some traingles are given below .which of them are right angled (i)a=15cm,b=20cm,c=25cm (ii)a=9cm,b=12cm,c=16cm (iii)a=10cm,b=24cm,c=26cm answer with explanation ​

Answer 1

$\sf\large\underline{Given:-}$

$\tt{\implies a=15cm\:\:,b=20cm\:\:,c=25cm}$

$\tt{\implies a=9cm\:\:,b=12cm\:\:,c=16cm}$

$\tt{\implies a=10cm\:\:,b=24cm\:\:,c=26cm}$

$\sf\large\underline{To\: Find:-}$

$\sf{\implies which\:is\: right\:angle\triangle:-}$

$\sf\large\underline{Solution:-}$

To calculate the right angle triangle at first we have to know how to find the right angle triangle. As we know that in right angle triangle the sum two square sides of triangle is equal to the square third side of triangle. In which two sides are perpendicular and base and the third side is hypotenuse. By applying Pythagoras theorem to find easily the given sides of triangle is right angle triangle or not.

$\sf\large\underline{Formula\: used:-}$

$\tt{\implies a=15cm\:\:,b=20cm\:\:,c=25cm}$

$\sf{\implies here,\:a=p\:\:,b=b\:\:,c=h}$

$\tt{\implies P^2+B^2=H^2}$

$\tt{\implies 15^2+20^2=25^2}$

$\tt{\implies 225+400=625}$

$\tt{\implies 625=625}$

$\sf\large\underline{Conclusion:-}$

Yes this is right angle triangle because it works on the given Question so, as per the Pythagoras theorem both sides are equal then it is said to be a right angle triangle.

$\tt{\implies a=9cm\:\:,b=12cm\:\:,c=16cm}$

$\sf{\implies here,\:a=p\:\:,b=b\:\:,c=h}$

$\tt{\implies P^2+B^2}$

$\tt{\implies 9^2+12^2}$

$\tt{\implies 81+144}$

$\tt{\implies 225}$

$\tt{\implies H^2=16^2=256}$

$\sf{\implies LHS\:\neq\:RHS}$

$\sf\large\underline{Conclusion:-}$

No this is not right angle triangle because it doesn't work on the given Question so, as per the Pythagoras theorem both sides are not equal then it is not said to be a right angle triangle.

$\tt{\implies a=10cm\:\:,b=24cm\:\:,c=26cm}$

$\sf{\implies here,\:a=p\:\:,b=b\:\:,c=h}$

$\tt{\implies P^2+B^2=H^2}$

$\tt{\implies 10^2+24^2=26^2}$

$\tt{\implies 100+576=676}$

$\tt{\implies 676=676}$

$\sf\large\underline{Conclusion:-}$

Yes this is right angle triangle because it works on the given Question so, as per the Pythagoras theorem both sides are equal then it is said to be a right angle triangle.

Answer 2

Step-by-step explanation:

I said this...

1) yes

2) no

3) yes