Answer: length = 82 feets
Width = 46 feets
Explanation:
The shape of the playground is rectangular. The perimeter of the playground is 256 feets. This means that the distance round the playground is 256 feets. The rectangular playground has length, l and width, w. The perimeter will be
L+L+W+W = 2L + 2W
2L + 2W = 256 - - - - - - - -1
The area of the playground is 3772 square feet. The area is determined by multiplying length and width of the playground.
L×W = 3772
LW = 3772
L = 3772/W
Substituting L = 3772/W
2(3772/W) + 2W = 256
7544/W + 2W = 256
7544 + 2W^2 = 256W
2W^2 - 256W + 7544 = 0
W^2 - 128W + 3772= 0
Using the general formula for quadratic equations
W = [-b +-√(b^2-4ac)] / 2a
a = 1
b = -128
c = 3772
W = [- -128 +-√(-128^2-4×1×3772)] / 2×1
W= [128 +-√(16384 - 15088)] / 2
W= [128 +-√(1296] / 2
W = (126+36)/2. or W = (126-36)/2
W = 82 or W = 46
L = 3772/82 or L = 3772/46
L = 46 or L = 82