Question

The sides of a triangle are 3 consecutive odd integers and the shortest side is 20% of the perimeter of the triangle. What is the perimeter of the triangle?

Answer 1

15 units

Explanation:

The terms of an odd integer are given by 2n - 1. Since the sides of the triangle are three consecutive odd integers, let them be 2n - 1, 2(n + 1) - 1 and 2(n + 2) - 1 respectively, where 2n - 1 is the shortest side

Let P = perimeter of triangle = 2n - 1 + 2(n + 1) - 1 + 2(n + 2) - 1

= 2n - 1 + 2n + 2 - 1 + 2n + 4 - 1

= 2n - 1 + 2n + 1 + 2n + 3

= 2n + 2n + 2n - 1 + 1 + 3

= 6n + 3

Since the shortest side is 20% of the perimeter of the triangle, we have that

2n - 1 = 20%(6n + 3)

2n - 1 = 0.2(6n + 3)

expanding the bracket, we have

2n - 1 = 1.2n + 0.6

subtracting -1.2n and adding +1 to both sides, we have

2n - 1.2n = 1 + 0.6

0.8n = 1.6

dividing both sides by 0.8, we have

n = 1.6/0.8

n = 2

Since P = 6n + 3, substituting n = 2, we have

P = 6(2) + 3 = 12 + 3 = 15 units