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A rectangular public park has an area of 3,600 square feet.
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27 May 2018, 12:22
27 May 2018, 12:22
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Question Stats:
46% (02:06) correct
53% (02:41) wrong based on 77 sessions
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A rectangular public park has an area of 3,600 square feet. It is surrounded on three sides by a chain link fence. If the entire length of the fence measures 180 feet, how many feet long could the unfenced side of the rectangular park be?
Indicate all such lengths.
A. 30
B. 40
C. 60
D. 90
E. 120
Indicate all such lengths.
A. 30
B. 40
C. 60
D. 90
E. 120
Re: A rectangular public park has an area of 3,600 square feet.
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27 May 2018, 13:16
27 May 2018, 13:16
3
1
Expert Reply
Explanation
The two values given are the area of the park and three out of the four sides of the perimeter of the park. If the side without fencing is a length, the equation for the overall length of the existing fence is 180 = 2W + L, so L = 180 – 2W.
The equation for the area of the park is LW = 3,600. With two variables and two equations, it is now possible to solve for the possible values of L:
\(L \times W = 3,600 L = 180 - 2W\)
\((180 - 2W)W = 3,600\)
\(180W - 2W^2 = 3,600\)
\(90W - W^2 = 1,800\)
\(0 = W^2 - 90W + 1,800\)
\(0 = (W - 60)(W - 30)\)
So W = 30 or 60. Plug each value back into either of the original two equations to solve for the corresponding length, which is 120 or 60, respectively.
The two values given are the area of the park and three out of the four sides of the perimeter of the park. If the side without fencing is a length, the equation for the overall length of the existing fence is 180 = 2W + L, so L = 180 – 2W.
The equation for the area of the park is LW = 3,600. With two variables and two equations, it is now possible to solve for the possible values of L:
\(L \times W = 3,600 L = 180 - 2W\)
\((180 - 2W)W = 3,600\)
\(180W - 2W^2 = 3,600\)
\(90W - W^2 = 1,800\)
\(0 = W^2 - 90W + 1,800\)
\(0 = (W - 60)(W - 30)\)
So W = 30 or 60. Plug each value back into either of the original two equations to solve for the corresponding length, which is 120 or 60, respectively.
Re: A rectangular public park has an area of 3,600 square feet.
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19 Jul 2020, 05:05
19 Jul 2020, 05:05
3
There is something wrong here. sandy's explanation is correct, but nowhere does the question say exactly which side of the park is left unfenced. It could well be either length or width of the park. If we consider only length, as sandy writes, sure it is either 120 or 60. But we also have to consider the possibility that the unfenced side is the width, which is either 30 or 60. Hence, 30 has got to be one of the possibilities. Surely, the answers are A, C, E?
