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.

Respuesta :

Answer:

x = 1

Step-by-step explanation:

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

[tex]4 \times (4x \: - 1) \: = 16x \: - \: 4[/tex]

Then, the perimeter of the rectangle will be =

[tex]2 \times (2x \: + \: 1) + \: 2 \times (x \: + 2) \\ = (4x \: + 2) + (2x \: + 4) [/tex]

By collecting like terms, we'll have:

[tex]4x + 2x \: + 2 + 4 \\ = 6x + 6[/tex]

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

[tex]16x \: - 4 = 6x + 6[/tex]

Collect like terms:

[tex]16x - 6x \: = \: 6 + 4 \\ 10x = 10[/tex]

Now, divide both sides by 10:

[tex] \frac{10x}{10} = \frac{10}{10 } \\ x = 1. [/tex]

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