Question

A pentagon has 3 congruent sides and 2 other congruent sides. The perimeter of the pentagon is 36 centimeters. The three long congruent sides are 2 centimeters longer than the two shorter congruent sides.

Let x = length of a short side
Let y = length of a long side

The system of equations can be used to represent the situation.

y = x + 2
2x + 3y = 36

What is the length of one of the shorter congruent sides?

Answer 1

Length of one of the shorter congruent side is: 6 cm

Explanation:

In order to find the length of congruent sides we have to solve the system of equations

Given systems of equation is:

y = x + 2

2x + 3y = 36

Putting y = x+2 in second equation

`2x + 3(x+2) = 36\\2x+3x+6 = 36\\5x+6 = 36\\5x = 36-6\\5x = 30\\(5x)/(5) = (30)/(5)\\x =6`

As we know that x represents the shorter side, the length of short side is: 6 cm

Hence,

Length of one of the shorter congruent side is: 6 cm