Question

The sides of a triangle are in the ratio 2 : 3: 4 and the longest side is 20 centimetres longer than the shortest side. Compute the length of each side.

Answer 1

Ratio of the sides of the triangle = 2:3:4

Let the length of the shortest side be a cm.

Length of the longest side = (a + 20) cm

Ratio of the length of the longest side to the shortest side = 4:2

∴ Length of the shortest side = a = 20 cm

Length of the longest side = (a + 20) cm = (20 + 20) cm = 40 cm

Ratio of the length of the longest side to the third side = 4:3

⇒ Length of the third side = × Length of the longest side

= × 40 cm

= 3 × 10 cm

= 30 cm

Thus, the lengths of the sides of the triangle are 20 cm, 30 cm and 40 cm.