Question

An isosceles triangle has a perimeter of 36 inches. Its base is 2

1
2
times longer than each of its legs. What are the lengths of the sides of the triangle?

Answer 1

The lengths of the sides of the triangle are 8, 8, 20

Step-by-step explanation:

Given that the perimeter of an isosceles triangle is 36 inches.

The base of the triangle is
`2(1)/(2)` times longer than each of its legs.

We need to determine the lengths of the sides of the triangle.

Lengths of the sides:

Let x denote the lengths of the sides of the triangle.

The base of the triangle is given by

`2(1)/(2)x=(5)/(2)x=2.5x`

Perimeter of the isosceles triangle = Sum of the three sides of the triangle.

Thus, we have,

`36=x+x+2.5x`

`36=4.5x`

`8=x`

Thus, the length of the sides of the isosceles triangle is 8 inches.

Base of the triangle =
`2.5(8)=20 \ inches`

Hence, the three sides of the isosceles triangle are 8, 8, 20