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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

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Question Stats:

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.
[#permalink]
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.
[#permalink]
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?

Re: A rectangular public park has an area of 3,600 square feet.
[#permalink]
19 Jul 2020, 07:58

Expert Reply

The spoiler says C and E

Re: A rectangular public park has an area of 3,600 square feet.
[#permalink]
07 Aug 2021, 09:10

2

NWaitforitZ wrote:

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?

option A cannot because it voilates the contraint of 180 unit sum of three side.

let see, 30 unit is unfenced side means other side must be 120. And given condition sum of three side exceed which violate the given condition.

Re: A rectangular public park has an area of 3,600 square feet.
[#permalink]
20 Jun 2024, 23:10

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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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