Question

A triangle has a perimeter of 165 cm. The first side is 65 cm less than twice the second side. The third side is 10 cm less than the second side. Find the length of each side of the triangle.

Answer 1

• first side: 55 cm
• second side: 60 cm
• third side: 50 cm

Explanation:

The problem statement gives all the side lengths in terms of that of the second side. Let s represent the length of the second side in cm. Then the length of the first side is (2s-65), and the length of the third side is (s-10). The perimeter is the sum of all the side lengths:

165 = (2s -65) +s +(s-10)

165 = 4s-75

240 = 4s

60 = s . . . . . . . . second side

2s-65 = 55 . . . . first side

s-10 = 50 . . . . . . third side

In order, the side lengths are 55 cm, 60 cm, 50 cm.