Question

The sides of certain triangles are given below. Determine which of them are right triangles
(i) a = 7 cm, b = 24 cm and c= 25 cm
(ii) a = 9 cm, b = 16 cm and c = 18 cm

Answer 1

(i) We know that in a right angled triangle, the square of the largest side is equal to the sum of the squares of the smaller sides.

Here, the larger side is c, which is 25 cm.

$c^2=625$

Given that,

$a^2+b^2=7^2+{24}^2$

$=49+576=625=c^2$

Thus, the given triangle is a right triangle.

(ii) We know that in a right angled triangle, the square of the largest side is equal to the sum of the squares of the smaller sides.

Here, the larger side is c, which is 18 cm.

$c^2=324$

Given that

$a^2+b^2=9^2+{16}^2$

$=81+256$

= 337 which is not equal to $c^2$

Thus, the given triangle is not a right triangle.