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# A rectangular public park has an area of 3,600 square feet.

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A rectangular public park has an area of 3,600 square feet. [#permalink]  27 May 2018, 12:22
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Question Stats:

60% (02:23) correct 40% (00:46) wrong based on 5 sessions
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
[Reveal] Spoiler: OA

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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4704
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 90

Kudos [?]: 1600 [0], given: 373

Re: A rectangular public park has an area of 3,600 square feet. [#permalink]  27 May 2018, 13:16
Expert's post
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.
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Re: A rectangular public park has an area of 3,600 square feet.   [#permalink] 27 May 2018, 13:16
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