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

Answer:

x = 1

Step-by-step explanation:

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

$4 \times (4x \: - 1) \: = 16x \: - \: 4$

Then, the perimeter of the rectangle will be =

$2 \times (2x \: + \: 1) + \: 2 \times (x \: + 2) \\ = (4x \: + 2) + (2x \: + 4)$

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:

$\frac{10x}{10} = \frac{10}{10 } \\ x = 1.$