Question

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. Write and solve an equation to find x.

Answer 1

step 1

the perimeter of square is

P=4b

where b is the length side

we have

b=4x-1

so

P=4(4x-1)

P=16x-4

step 2

The perimeter of rectangle is equal to

P=2(L+W)

we have

L=2x+2

W=2x

substitute

P=2(2x+2+2x)

P=2(4x+2)

P=8x+4

step 3

equate the perimeters

16x-4=8x+4

solve for x

16x-8x=4+4

8x=8

x=1