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A thin strip [#permalink]
1
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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