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

`x = 12`

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 = (24)/(2)`

`x = 12`