A square and a rectangle have the same perimeter. The square has a side length of 8x units. The rectangle has a length of (10x+8) units and a width of 10 units. What will be the perimeter of either the rectangle and the square?

Well we know that the perimeters are equal so:

Psquare = Prectangle

we know perimeter for square is the 4 sides of same lengths added up or 4*s

the perimeter of a rectangle is the then4 sides with 2 being equal added up so 2*L + 2*W

we know that a square side equAls s and it says that s=8x. So:

Psqu = 4 * (8x) (substitute 8x for s)

we know that the rectangle L = 10x + 8 and W = 10. So

Prect = 2 * (10x + 8) + 2 * (10)

we know:

Prect = Psqu so:

4 * (8x) = 2 * (10x + 8) + 2 * (10)

32x = 20x + 16 + 20

12x = 36

x = 3

So if x equals 3 we can sub x in for square perimeter

Psqu = 4 * (8 * 3)

P = 4 * 24

P = 96

we can check this with rectangle perimeter

P = 2 * (10 * 3 + 8) + 2 * 10

P = 2 * 38 + 20

P = 96