Question

Robert has 60 feet of fence to make a dog pen. He will use the house for one side of the pen, as shown above. What dimensions will make the largest pen?
A.
10 ft by 40 ft
B.
12 ft by 36 ft
C.
15 ft by 30 ft
D.
20 ft by 20 ft

Answer 1

The formula for an area of a regular parallelogram is:

A = l * w

Where,

l = length

w = width

We are given that the total measurement of fence is only 60 feet and one side of the house is used as one side of the pen. Therefore,

l + 2 w = 60

or simplifying to make an explicit expression for one  variable, say l:

l = 60 – 2 w

Substituting to the 1st equation:

A = (60 – 2 w) * w

A = 60 w – 2 w^2

The maxima are obtained by getting the 1st derivative then equating dA/dw = 0:

dA/dw = 60 – 4 w

60 – 4 w = 0

4 w = 60

w = 15

Since l = 60 - 2w

l = 60 – 30

l = 30

Therefore the dimension that will make the largest pen is 15 ft by 30 ft.

ANSWER: C