Question

A square and an equilateral triangle have a combined perimeter of 101 inches. The side length of the triangle is 8 inches less than twice the side length of the square. What is the perimeter of the square?

Answer 1

Explanation:

let length of square=x in

then length of equilateral triangle=2x-8

p (square)=4x

P(triangle=3(2x-8)=6x-24

4x+6x-24=101

10x=101+24=125

x=12.5

perimeter of square=4x=4*12.5=50 inches.

Answer 2

Explanation:

Let x represent the side length of the square.

Let y represent the side length of the equilateral triangle.

A square and an equilateral triangle have a combined perimeter of 101 inches. It means that

4x + 3y = 101

The side length of the triangle is 8 inches less than twice the side length of the square. This means that

y = 2x - 8

Substituting y = 2x - 8 into equation 1, it becomes

4x + 3(2x - 8) = 101

4x + 6x - 24 = 101

10x = 101 + 24

x = 125/10 = 12.5

y = 2x - 8 = 2 × 12.5 - 8

y = 25 - 8 = 13

Therefore, perimeter of the square is

4 × 1.2. 5 = 50 inches