# Sides of some triangles are given below. Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse (i) 7 cm, 24 cm, 25 cm (ii) 3 cm, 8 cm, 6 cm (iii) 50 cm, 80 cm, 100 cm (iv) 13 cm, 12 cm, 5 cm

## Solution :

(i) 7 cm, 24 cm, 25 cm

Let AB = 7 cm, BC = 24 cm, CA = 25 cm

then  $${AB}^2$$ = 49,  $${BC}^2$$ = 576  and  $${CA}^2$$ = 625

$${AB}^2$$ + $${BC}^2$$ = 625 = $${CA}^2$$

Yes, ABC is a right triangle and its hypotenuse is 25 cm.

(ii) 3 cm, 8 cm, 6 cm

Let AB = 3 cm, BC = 8 cm, CA = 6 cm

then  $${AB}^2$$ = 9,  $${BC}^2$$ = 64  and  $${CA}^2$$ = 36

$${AB}^2$$ + $${CA}^2$$ = 45 $$\ne$$ $${BC}^2$$

No, ABC is not a right triangle.

(iii) 50 cm, 80 cm, 100 cm

Let AB =  50 cm, BC = 80 cm, CA = 100 cm

then  $${AB}^2$$ = 2500,  $${BC}^2$$ = 6400  and  $${CA}^2$$ = 10000

$${AB}^2$$ + $${BC}^2$$ = 8900 $$\ne$$ $${CA}^2$$

No, ABC is not a right triangle.

(iv) 13 cm, 12 cm, 5 cm

Let AB = 13 cm, BC = 12 cm, CA = 5 cm

then  $${AB}^2$$ = 169,  $${BC}^2$$ = 144  and  $${CA}^2$$ = 25

$${BC}^2$$ + $${CA}^2$$ = 169 = $${AB}^2$$

Yes, ABC is a right triangle and its hypotenuse is 13 cm.