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