Question

Vikas wishes to fit three rods together in a shape of the right triangle. The hypotenuse is to be 2 cm longer than the base and 4 cm longer than the altitude. What should be the lengths of the rods?

Answer 1

Let the base of the right triangle be x cm.

Hypotenuse = x + 2 cm

Since hypotenuse is 4 cm longer than the altitude,

Altitude = (x + 2) − 4 = x − 2 cm

For a right-angled triangle:

(Hypotenuse)² = (Base)² + (Altitude)²

(x + 2)² = x² + (x − 2)²

x² + 4x + 4 = x² + (x² − 4x + 4)

x² + 4x + 4 = 2x² − 4x + 4

0 = x² − 8x

x(x − 8) = 0

x = 8 (reject x = 0)

Find lengths of the rods

Base = x = 8 cm

Altitude = x − 2 = 6 cm

Hypotenuse = x + 2 = 10 cm​

The lengths of the three rods are:

6 cm, 8 cm, 10 cm​