a square and a rectangle have equal perimeters. The length of a side of the square is 4x- 1. The length of the rectangle is 2x + 2 and the width is 2x. Right and solve an equation to find the value of x in the perimeter of the square.

x = 1

Step-by-step explanation:

Perimeter of a square -> p = 4s (p stands for perimeter and s stands for side length)

Plug that in with s = 4x-1 (length of one side of the square) ->

p = 4 (4x-1)

We use the distributive property to get ->

p = 4 (4x) - 4(1)

  = 16x - 4

We now know that the perimeter of the square is 16x - 4.

Since we know that the perimeter of the square and rectangle are equal (the problem told us), we can use this and plug the length and width of the rectangle in. Formula for rectangles are -> p = 2 (s1 + s2) (s1 is the length, s2 is the width) (p stands for perimeter and s stands for side length).

p (perimeter) -> 16x - 4

s1 (length) -> 2x +2

s2 (width) -> 2x

Let's plug our answers in:

16x - 4 = 2( 2x + 2 + 2x)

Combine like terms:

16x - 4 = 2 (4x + 2)

Use the distributive property:

16x - 4 = 2 (4x) + 2 (2)

Simplify:

16x - 4 = 8x +4

Inverse Operations:

16x - 4 - 8x = 8x +4 -8x

Combine like terms:

8x - 4 = 4

Inverse Operations:

8x - 4 + 4 = 4 + 4

Simplify:

8x = 8

Divide:

8x / 8 = 8 / 8

Simplify:

x = 1

If you have any questions, feel free to ask me (or anyone else)! Good luck!

step-by-step explanation: s