The playground at school is rectangular, and each dimension is a whole number. the playgrounds area is 3772 square feet, and it's perimeter is 256 feet. what are the dimensions of the playground?

length = 82 feets

Width = 46 feets

Step-by-step 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

m a t h w a y. c o m

step-by-step explanation: