Question

A farmer has 1,700 feet of fence and wishes to build two identical rectangular enclosures, as in the following figure. What should be the dimensions of each enclosure if the total area is to be a maximum? What is the area of each enclosure?Answer with an exact fraction or round to the nearest whole number.



Each enclosure will have width (shortest side) of  feet, length (longest side) of  feet and area of  square feet.

Answer 1

Let's assume

length of each rectangle =x

width of each rectangle =y

we are given

A farmer has 1,700 feet of fence and wishes to build two identical rectangular enclosures

so, we can set up equation as

now, we can solve for y

now, we can find area

now, we can find derivative

now, we can set it to 0

and then we can solve for x

now, we can find y

Dimensions:

Length of each rectangle = 212.5 feet

Width of each rectangle = 212.5 feet

Area:

now, we can find area