A farmer decides to enclose a rectangular garden, using the side of a barn as one side of the rectangle. What is the maximum area that the farmer can enclose with 80 feet of fence? What should the dimensions of the garden be to give the area?

Garden

max area is if the sides are as equal as possible

so he should try to make a square (ideal is a circle, but barn walls are normally straight)

squaer perimiter=4 times legnth of 1 side

perimiter=amount of fencing=80

80=4s

divide 4

20=s

one sides=20

area=legnth times width

in squaer, legnth=width

20=legnth

20=width

area=20 times 20=400

dimetions are 20ft by 20ft to give 400ft^2

(fun fact, if it were a circle, the area would be about 509.5ft^2)

answer is 20ft by 20ft and area=400ft^2