Question 858550: The owner of a parking lot is going to enclose a rectangular area with fencing using an existing fence and entry gate as one of the sides. The owner has 220 feet of new fencing material (which is much less than the length of the existing fence).
A. What is the maximum possible area that the owner can enclose? Make sure to include the equation.
B. What will be the dimensions of the enclosed parking lot?
C. If there is a driveway (20 feet wide) into the lot and each car stall measures 9 feet by 20 feet could 30 cars be parked in the lot if no car is parked on the driveway? Using complete sentences, explain your answer.
Answer by JulietG(1812)   (Show Source):
You can put this solution on YOUR website! This is an impossible scenario because of this line: the owner has 220 feet of new fencing material (which is much less than the length of the existing fence). If the length of the existing fence is more than 220, then the perimeter cannot be a rectangle enclosed with an additional 220 ft. The 220 ft won't fit into the perimeter equation: P = 2L + 2W.
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We'll solve it without the parenthetical comment.
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220 = 2W + 1L (the other L is existing)
Since the numbers closest to each other will produce the largest area, let's divide 220 by 3 sides, rounding to whole numbers. 74, 73, 73, with an existing 74.
Perimeter = 2W + 2L
L = 74 (with the existing fence as L)
W = 73
Area = 74 * 73 = 5402
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If the car stalls measure 9 * 20, then they take up 180sf each.
180 * 3 = 5400
Yes, they could be parked there with 2 sf left over.
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