Question

David loves his dog Thor and he wants to create a rectangular enclosure that has an area of 1600ft² for the dog to stay in while no one is home. David has a total of 120 feet of fencing available and he wants to use the wall of his garage as one of the sides of the enclosure. What are the dimensions of the enclosure?

Make a Sketch of the rectangular enclosure and label the sides using variable(s).

Write and solve an equation(s) that model this situation.

What are the dimensions of the rectangular enclosure?

Answer 1

80 feet by 20 feet

Explanation:

Area of the rectangular enclosure = 1600ft²

Area, lw=1600

w=1600/l

Perimeter, 2w+l=120 feet

Substituting w=1600/l into the perimeter

2(1600/l)+l=120

3200/l+l=120

`(3200+l^2)/(l)=120\\ 3200+l^2=120l\\l^2-120l+3200=0\\l^2-40l-80l+3200=0\\l(l-40)-80(l-40)=0\\(l-40)(l-80)=0\\l-40=0\:or\:l-80=0\\l=40\:or\:l=80`

When l=40, w=1600/40=40 feet

When l=80, w=1600/80=20 feet

Since the enclosure is rectangular, the acceptable dimensions are:

Length =80 feet

Width =20 feet