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A thin strip

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SamaunParvez
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A thin strip [#permalink] New post   20 Mar 2021, 05:19
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A thin strip of binding 30 feet long just fits around the perimeter of a rectangular rug that covers an area of 54 square feet.


Quantity A
Quantity B
The length of the longer side of the rug
10 feet


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
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A thin strip [#permalink] New post   20 Mar 2021, 07:09
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First of all when you post a question, be careful to post under the right sub forum and to follow the rules how to format properly the question

here for reference https://gre.myprepclub.com/forum/how-to-po ... 12752.html
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Re: A thin strip [#permalink] New post   20 Mar 2021, 07:10
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Area: xy=54
Perimeter: 2(x+y)=30
Solve these 2 simultaneous equations.
x=9,6 ; y=6,9
so length of longer side = 9
B
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A thin strip [#permalink] New post   20 Mar 2021, 23:44
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SamaunParvez wrote:
A thin strip of binding 30 feet long just fits around the perimeter of a rectangular rug that covers an area of 54 square feet.


Quantity A
Quantity B
The length of the longer side of the rug
10 feet


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


Let the length of the longer side be \(L\) and that of shorter side be \(B\)

Given, \( LB = 54\) and \(2(L + B) = 30\)

\(B = \frac{54}{L}\)

\(L + B = 15\)

\(L + \frac{54}{L} = 15\)

\(L^2 - 15L + 54 = 0\)

\((L - 9)(L - 6) = 0\)

\(L = 9\) or \(L = 6\)

NOTE: \(L\) cannot be \(6\) - because it will make \(B\) as \(9\) where \(L < B\)

Col. A: \(9\)
Col. B: \(10\)

Hence, option B
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A thin strip [#permalink]
20 Mar 2021, 23:44
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