rectangular question

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EddieU: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Sun May 22, 2011 4:53 amFollowed by: 1 member; Thanked: 1 times

by EddieU » Wed Jun 15, 2011 6:29 pm

HI,
can anyone please post how to answer the problem below? Don't we need to know the width of the frame to answer the question?
Correct answer: A.

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Source: Beat The GMAT — Problem Solving | Wed Jun 15, 2011 6:29 pm

champ0007: Senior | Next Rank: 100 Posts; Posts: 43; Joined: Wed Feb 06, 2008 5:37 amFollowed by: 1 member; Thanked: 8 times

by champ0007 » Wed Jun 15, 2011 6:58 pm

Assume the length and breadth of the picture to be L and B respectively.

Area of the picture = LB
Area of frame = 18 * 15 - Area of picture = 270 - LB

Condition 1 - Area of picture is equal to area of the frame
therefore, LB = 270 - LB
2LB = 270
LB = 135 ------(1)

Condition 2
L/B = 18/15
L/B = 6/5 ------ (2)

Combining the 2 equations
B = 5L/6
substitute this in equation 1
(5 * L^2)/6 = 135
L^2 = 27 * 6 = 162 = 81 * 2
L = 9(Sqrt(2))

So, Answer A !

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