A rectangular shaped garden has a perimeter of 66ft and area of 216ft. Find the dimensions

The perimeter is then

2L + 2W = 66

The area is

L*W = 216

Solve the first equation for L

2L = 66 - 2W

L = 66/2 - 2W/2 = 33 - W

Put this into the second equation

(33 - W) * W = 216

33W - W^2 = 216

rearranging

W^2 - 33W + 216 = 0

Using the quadratic formula

[ - (-33) plus or minus sqrt ((-33) * (-33) - 4 * 1 * 216) ]/2

[33 plus or minus sqrt (1089 - 864) ]/2

[33 plus or minus sqrt (225) ]/2

[33 plus or minus 15]/2

(33 + 15) / 2 = 48/3 = 16 = W

(33 - 15) / 2 = 18/2 = 9 = W

Checking back into the original equations

L = 24 W = 9