Question

Two equal sides of a triangle are each 4 m less than three times the third side. Find the dimensions of the triangle, if its perimeter is 55 m.

Answer 1

Let the third side of triangle be x m.

Then, two equal sides of triangle = (3x – 4) m

Given, perimeter of triangle = 55 m

∵ Perimeter of a triangle = Sum of the sides of the triangle

∴ x + 3x – 4 + 3x – 4 = 55

⇒ 7x – 8 = 55

⇒ 7x = 55 + 8

⇒ 7x = 63

⇒ x = `63/7`

∴ x = 9

Hence, the dimensions of the triangle are 9 m, (3 × 9 – 4) m and (3 × 9 – 4) m, i.e. 9, (27 – 4) and (27 – 4) m, i.e. 9 m, 23 m and 23 m.