Question

You want to fence off a rectangular area of yard using the back side of your house as one of the sides. You have a total of 150 yards of fence. If the area of the fenced in portion comes to 2,812 square yards, what are the dimensions of the fenced-in area? Show all work for full credit.

Answer 1

Let the length of the Area be 'L'

and the width of the house be 'B'

The dimensions of the fence can be

L = 37 yards and B = 76 yards

or

L = 38 yards and B = 76 yards

Explanation:

Let the length of the Area be 'L'

and the width of the house be 'B'

Data provided in the question:

Total length of the fence = 150 yards

also,

Perimeter of the fence = 2L + B [because one side is fenced using back side of the house thus single 'B' instead of 2B]

thus,

2L + B = 150

or

B = 150 - 2L ...........(1)

And,

The fenced-in area = 2,812 square yards

also,

The fenced-in area = L × B

thus,

L × B = 2,812

from 1

L × ( 150 - 2L ) = 2,812

or

150L - 2L² = 2,812

or

2L² - 150L + 2,812 = 0

or

or

L² - 75L + 1406 = 0

or

L² - 37L - 38L + 1406 = 0

or

L ( L - 37 ) - 38 ( L - 37 ) = 0

or

( L - 37 ) × ( L -38 ) = 0

or

L = 37 or L = 38 yards

Thus,

B = 150 - 2L

for, L = 37 yards

B = 150 - 2 × 37 = 76 yards

and,

For L = 38 yards

B = 150 - 2 × 38 = 74 yards

Therefore,

The dimensions of the fence can be

L = 37 yards and B = 76 yards

or

L = 38 yards and B = 76 yards