Question

Jamal wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn, so he needs no fence on that side. The other three sides will be enclosed with wire fencing. If Jamal has 700 feet of fencing, you can find the dimensions that maximize the area of the enclosure.
a) Let w be the width of the enclosure (perpendicular to the barn) and let l be the length of the enclosure (parallel to the barn). Write an function for the area A of the enclosure in terms of w . (HINT first write

Answer 1

Answer:

Area of the rectangle = 700 - 2w²

Step-by-step explanation:

In the picture attached one side of the rectangle is Barn.

Two perpendicular sides of the barn are width 'w' and one parallel side to the barn is 'l'.

Jamal has the fencing having length = 700 feet

So, to cover three sides of the rectangle length of wire required = (2w + l) feet

This length should be equal to the length of the wire, which is to be used to cover these three sides.

(2w + l) = 700

l = 700 - 2w ------(1)

Area of the rectangle = lw

By replacing the value of l from equation 1

Area = w(700 - 2w)

Area = 700w - 2w²