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

The shorter side of pentagon is 6cm long

Explanation:

Given two equations are:

`y = x + 2\\2x + 3y = 36`

We can use any one of the methods to solve the simultaneous linear equations

As it is also given that x is the length of shorter side, we have to find the value of x

Using the substitution method

We will put the value of y i.e. x+2 in the 2nd equation

So,

`2x+3(x+2) = 36`

Simplification gives us:

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

Hence,

The shorter side of pentagon is 6cm long