SOLUTION: Jonathan has 1000 feet of fencing available to fence in the rectangular yard next to his house. What is the maximum enclosed area if the side along his house does NOT need to be f

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Question 1198363: Jonathan has 1000 feet of fencing available to fence in the rectangular yard next to his house. What is the maximum enclosed area if the side along his house does NOT need to be fenced?
Which of the following is correct?
A) 6,250 square feet
B) 1,250 square feet
C) 62,500 square feet
D) 125,000 square feet
E) 625 square feet

Found 2 solutions by ikleyn, ewatrrr:
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
Jonathan has 1000 feet of fencing available to fence in the rectangular yard next to his house.
What is the maximum enclosed area if the side along his house does NOT need to be fenced?
Which of the following is correct?
A) 6,250 square feet
B) 1,250 square feet
C) 62,500 square feet
D) 125,000 square feet
E) 625 square feet
~~~~~~~~~~~~~~~~~~~


Formally, the yard should have dimensions 250 ft x 500 ft,
where 500 ft is the length along the house.

But I hesitate to go out with this answer, since I am not sure that Jonatan's house is so long.

I hesitate that people will laugh on me, if I say that Jonatan's house is more than 500 ft long.


People may say that I lost my mind and my common sense, while I am not.




Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
1000ft fencing: 3-sided
A = x(1000-2x)
A' = 1000 - 4x
Maximize: 4x = 1000
x = 250ft
A = 250ft*500ft = 125,000ft^2
Agree: 500ft is a hefty number for a length of a house.

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