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]