I need help on this math problem dude

Question

A square and a rectangle have the same parameters. The length of a side of the square is 4x-1. The length of the rectangle is 2x+1 and the width is x+2. Write and solve an equation to find X.

Answer 1

Here's what we know:

P_squ = 4s (perimeter of a square are all 4 sides added together (or 1 side times 4))

P_rec = 2L + 2w (perimeter of a rectangle is the 2 length plus 2 widths)

P_squ = P_rec (the two perimeters are the same lengths around)

s = 4x - 1

L = 2x + 1

w = x + 2

We have values for our variables, so plug them in:

4(4x - 1) = 2(2x + 1) + 2(x + 2)

Distribute:

16x - 4 = 4x + 2 + 2x + 4

Combine like terms:

16x - 4 = 6x + 6

Subtract 6x:

16x - 4 - 6x = 6x + 6 - 6x

10x - 4 = 6

add 4:

10x - 4 + 4 = 6 + 4

10x = 10

divide by 10:

10x / 10 = 10 / 10

x = 1

check:

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

4(4 - 1) = 2(2 + 1) + 2(1 + 2)

4(3) = 2(3) + 2(3)

4(3) = 4(3)