Question

The lengths of the sides of triangles are given below. Which of them are right-angled?

(i) a = 15 cm, b = 20 cm and c = 25 cm
(ii) a = 9 cm, b = 12 cm and c = 16 cm
(iii) a = 10 cm, b = 24 cm and c = 26 cm

Answer 1

(i) Largest side, c = 25 cm

We have:
$a^2+$$b^2$ = 225 + 400 = 625

Also, $c^2$ = 625

∴ $a^2+$$b^2$ = $c^2$
Hence, the given triangle is right angled using the Pythagoras theorem.

(ii) Largest side, c = 16 cm
We have:
$a^2+$$b^2$ = 81 + 144 = 225

Also, $c^2$ = 256

Here, $a^2+$$b^2$ $\ne$$c^2$

Therefore, the given triangle is not right angled.

(iii) Largest side, c = 26 cm

We have:
$a^2+$$b^2$ = 100 + 576= 676

Also, $c^2$ = 676

∴ $a^2+$$b^2$ = $c^2$
Hence, the given triangle is right angled using the Pythagoras theorem.