Word Problem

Question

A gardener needs to enclose three adjacent rectangular gardens, one for tomatoes, one for squash, and one for pumpkin. If 400ft of fencing is available what is the largest total area that can be enclosed?

Answer 1

Draw a label a diagram!

The pen has a "top" and a "bottom." Represent each by t.

The pen has four "sides." Represent each by s

 

2t + 4s = 400

 

The area of each pen is st

A = st

 

2t + 4s = 400

2t = 400 - 4s

t = 200 - 2s

 

A = s(200 - 2s)

A = -4s² + 200s

 

Maximum occurs at -b/2a, or -200/-8, or 25

 

Each side is 25 feet. The top and bottom are each 150 feet.

 

Area equals 25 x 150.