Question

Suppose you are building a rectangular pen for your goats. You use 400 feet of fencing for the pen.

Answer 1

part A

The pen has a rectangular shape of length l and width, say w.

The perimeter (the fencing) of this rectangle is 2l+2w, as in the rectangle we have 2 opposing sides of length l and 2 opposing sides of length w.

This means that 2l+2w=400

subtract 2l from both sides:

2w=400-2l

divide by 2:

w=200-l, so we find that the width is 200-l.


part B

we are asked to find w when l=80 ft,

since we have w=200-l, we can find w for l=80 ft by substituting :

w=200-l=200-80=120  (feet)


Part C

The area of the pen when l=90 feet is:

$A_{pen}=width \cdot length=(200-l) \cdot l=(200-90) \cdot 90\\\\=110 \cdot 90=9,900$  (square feet)