Question

The length of the sides of a square measure 2x-5. The length of a rectangle measures 2x, and the width measures x + 2. For what value of x is the perimeter of the square the same as the perimeter of the rectangle?

Answer 1

Answer:

$x = 12$

Step-by-step explanation:

Perimeter of a square:

The perimeter of a square of side x is given by:

$P_s = 4x$

Perimeter of a rectangle:

The perimeter of a rectangle of length l and width w is given by:

$P_r = 2(l + w)$

The length of the sides of a square measure 2x-5.

This means that the perimeter of the square is:

$P_s = 4(2x - 5) = 8x - 20$

The length of a rectangle measures 2x, and the width measures x + 2.

This means that the perimeter of the rectangle is:

$P_r = 2(2x + x + 2) = 2(3x + 2) = 6x + 4$

For what value of x is the perimeter of the square the same as the perimeter of the rectangle?

This is x for which:

$P_s = P_r$

So

$8x - 20 = 6x + 4$

$8x - 6x = 20 + 4$

$2x = 24$

$x = \frac{24}{2}$

$x = 12$