The perimeter of the quadrilateral is 80feet. Find the length of the other sides.

One side is x+9 another is x+13, 4x-5, x^2-8x.

Let's just add up the four sides you gave

x+9 + x+13 + 4x-5 + x^2 - 8x = 80
x^2 -2x -63 = 0
(x-9)(x+7) = 0

x = 9 or x = -7

case1: x = 9
the sides are: 18 , 22 , 31 , and 9
check: 18+22+31+9 = 80

case 2: x = -7
the sides are: 2, 6 , -33 ---- makes no sense .....

the sides are
18 , 22 , 31 , and 9