Question

The altitude of a right angled triangle is 7 cm less than its base. If its hypotenuse is 17 cm long, then find the length of the sides of the triangle.

Answer 1

We have, x² − 7x − 120 = 0

By splitting the middle term, we get 

x² − 15x + 8x − 120 = 0

∴ x(x − 15)x + 8(x − 15) = 0

∴ (x − 15)(x + 8) = 0

∴ x − 15 = 0 or x + 8 = 0

∴ x = 15 or x = −8

But the sides of the triangle cannot be negative.

∴ x = 15 cm

Thus, the base of the triangle = x = 15 cm

and altitude of triangle = (x − 7)

= (15 − 7) cm

= 8 cm