Hello Guest!

Let's start by setting the sides of our rectangle as x and y.

2x + 2y = perimeter

x*y = area

Thus, our equation is x*y = 4(2x + 2y)

x*y = 4(2x + 2y)

x*y = 8x + 8y # Distribute

x*y - 8x - 8y # Subtract 8x + 8y to both sides

The next part is kinda complicated.

(x-8)(y-8) = xy - 8x - 8y + 64

So (x-8)(y-8) = -64

The smallest possible perimeter will be when x and y are very close, but since it's not a square, x and y can't be equal, x-8 and y-8 both must be positive integers too.

Out of our factors of -64, -8 and 8 are the closest to each other. However, this doesn't work because for y - 8 = -8, y is equal to 0.

The next closest factor is -4 and 16.

x - 8 = 16

x = 24

y - 8 = -4

y = 4

Thus, our side lengths are 4 and 16 making the perimeter 40. :)))

I hope this helped.

=^._.^=