Question

A square and a rectangle have the same perimeters. The length of a side of the square is 4x – 1. The length of the rectangle is 2x + 1 and the width is x + 2. Write and solve an equation to find x.

Answer 1

x = 1

Explanation:

Since a square has four sides the perimeter of the square is =

`4 * (4x \: - 1) \: = 16x \: - \: 4`

Then, the perimeter of the rectangle will be =

`2 * (2x \: + \: 1) + \: 2 * (x \: + 2) \\ = (4x \: + 2) + (2x \: + 4)`

By collecting like terms, we'll have:

`4x + 2x \: + 2 + 4 \\ = 6x + 6`

Therefore, to find the value of x, we will equate both perimeters:

`16x \: - 4 = 6x + 6`

Collect like terms:

`16x - 6x \: = \: 6 + 4 \\ 10x = 10`

Now, divide both sides by 10:

`(10x)/(10) = (10)/(10 ) \\ x = 1.`