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1,600 feet of fencing is used to enclose a square plot.

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1,600 feet of fencing is used to enclose a square plot. [#permalink] New post 19 Oct 2017, 14:49
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Question Stats:

77% (00:47) correct 22% (01:23) wrong based on 27 sessions


1,600 feet of fencing is used to enclose a square plot.

Quantity A
Quantity B
The plot's new area if the length were
reduced by 4 feet and the width
increased by 4 feet
The plot's new area if the length
were equal to 398 feet and the width
were equal to 402 feet


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: 1,600 feet of fencing is used to enclose a square plot. [#permalink] New post 20 Oct 2017, 06:45
Since the plot is a square, its side is equal to \(sqrt(1600) = 40\). Then quantity A is 36*44 = 1584. Quantity B, instead is 402*398 = 159,996.

Answer B
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Re: 1,600 feet of fencing is used to enclose a square plot. [#permalink] New post 04 Mar 2018, 06:42
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As per the question,
1600ft = perimeter of a square plot => length of each side = 1600/4 = 400ft

So,
Quantity A = (len-4)(len+4) = (400-4)(400+4) = 400^2 - 4^2
Quantity B = 398x402 = (400-2)(400+2) = 400^2 - 2^2
=> Quantity B > Quantity A
Hence answer is B.
Re: 1,600 feet of fencing is used to enclose a square plot.   [#permalink] 04 Mar 2018, 06:42
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1,600 feet of fencing is used to enclose a square plot.

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