Question

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

Answer 1

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