ratio difference between a square and a rectangle

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lukaswelker: Senior | Next Rank: 100 Posts; Posts: 65; Joined: Wed Mar 26, 2014 6:56 amFollowed by: 1 member

by lukaswelker » Tue Apr 08, 2014 10:26 am

Hey guys, I lost a sea once more

Here is the question,

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

25:16 - 24:25 - 5:6 - 4:5 - 4:9

Any suggestions?

Many thanks
Lukas

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Source: Beat The GMAT — Problem Solving | Tue Apr 08, 2014 10:26 am

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by GMATGuruNY » Tue Apr 08, 2014 10:40 am

The perimeters 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 are of region S ?

A 25:16
B 24:25
C 5:6
D 4:5
E 4:9

Since a square has 4 equal sides, plug in multiples of 4.

Rectangle R:
Since L:W = 2:3, let L = 4*2 = 8 and W = 4*3 = 12.
Then:
Perimeter = L+W+L+W = 8+12+8+12 = 40.
Area = L*W = 8*12 = 96.

Square S:
Since S and R have the same perimeter, P = 40.
Since perimeter = 40, S=10.
Area = SÂ² = 10Â² = 100.

Resulting ratio:
R/S = 96/100 = 48/50 = 24/25.

The correct answer is B.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Apr 08, 2014 10:42 am

The perimeters 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 are of region S ?

A 25:16
B 24:25
C 5:6
D 4:5
E 4:9

Let's PLUG IN some values that meet the given conditions.

The sides of R are in the ratio 2:3
So, let the two sides have lengths 2 and 3.
This means the area of Region R = (2)(3) = 6
This means the ENTIRE perimeter of Region R is 2 + 2 + 3 + 3 = 10

The perimeters of square region S and rectangular region R are equal.
This means the perimeter of square region S is also 10
Since all 4 sides in a square are of equal length, each side must have length 2.5
So, the area of Region S = (2.5)(2.5) = 6.25

What is the ratio of the area of region R to the are of region S ?
We get: 6 : 6.25
Check the answer choices .... no matches. So, we need to take 6 : 6.25 and find an equivalent ratio.
If we multiply both parts by 4 we get: 24 : 25
So, the correct answer is B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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