Geometryword problem

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mpaudena: Senior | Next Rank: 100 Posts; Posts: 80; Joined: Wed Jun 04, 2008 1:16 pm; Thanked: 3 times

by mpaudena » Fri Sep 18, 2009 10:14 am

The perimeter of square region S and rectangular region R are equal. If the sides of R are in the ratio 2: 3, what is the ratio of the area of region R to the area of region S?

A) 25: 16

B) 24: 25

C) 5: 6

D) 4: 5

E) 4: 9

Please tell me answer and how you arrived at the answer. Thanks.

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Source: Beat The GMAT — Problem Solving | Fri Sep 18, 2009 10:14 am

m&m: Master | Next Rank: 500 Posts; Posts: 134; Joined: Sun Feb 15, 2009 7:44 pm; Thanked: 14 times

by m&m » Fri Sep 18, 2009 10:24 am

if rectangle has ratio of 2:3 then 2x+3x+2x+3x = 10x is total perimeter. Then square has sides of 2.5x = 5/2x

so area is (2x*3x)/((5/2*x)*(5/2*x)) = 6/(25/4) = 6*4/25 = 24/25

so B

hope that helps

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mpaudena: Senior | Next Rank: 100 Posts; Posts: 80; Joined: Wed Jun 04, 2008 1:16 pm; Thanked: 3 times

by mpaudena » Fri Sep 18, 2009 11:14 am

U make it simply. That's awsome. Thanks.l

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