question listed below

Question

The square and a rectangle have the same perimeters . the length of a side of the square is 6x - 2. The length of the rectangle is 2x + 2 and the width is x + 3. write and solve an equation to find x.

Answer 1

Since the square has 4 sides of the same length, the perimeter of the square is 4(6x-2).

The rectangles perimeter will equal 2l+2w=2(2x+2)+2(x+3)

We know the perimeter of the two are equal to each other so you get

4(6x-2)=2(2x+2)+2(x+3)

24x-8=4x+4+2x+6

24x-8=6x+10 (add 8 and subtract 6x to both sides to put like terms together)

18x=18

X=1

Answer 2

Hi Matthew J.

Perimeter of a Square = 4s where s is the side

Perimeter of a Rectangle = 2L + 2W where L is the length and W is the Width

Since you are given that the Perimeter of the square and the rectangle are equal then

4s = 2L + 2W

Plug in the expressions you are given for the side of the square 6x -2, the length of the rectangle 2x + 2 and the width of the rectangle x + 3 and solve for x

4(6x -2) = 2(2x + 2) + 2(x + 3)

Divide both sides of the equation by 2

2(6x - 2) = 2x + 2 + x + 3

Multiply through the parentheses

12x - 4 = 2x + 2 + x + 3

Combine like terms

12x - 4 = 3x + 5

Isolate the variables on one side of the equation and the constants on the other

12x - 3x = 5 + 4

Combine like terms again

9x = 9

Divide both sides of the equation by 9

x = 1

To check plug this value into both equations for the perimeter of the square and the perimeter of the rectangle

4(6x - 2) = 2(2x + 2) + 2(x + 3)

4(6*1 - 2) = 2( 2*1 + 2) + 2(1 + 3)

4(6 -2) = 2(2 + 2) + 2(4)

4(4) = 2(4) + 2(4)

16 = 8 + 8

16 = 16

I hope this helps.