BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

GMAT Prep ?? (Geometry)

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 446
Joined: Thu Jul 26, 2007 1:07 pm
Thanked: 6 times

GMAT Prep ?? (Geometry)

by dferm » Fri May 09, 2008 6:48 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 area of region S?

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

Please help...

Thanks...
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 189
Joined: Thu May 01, 2008 10:55 pm
Location: Seattle, WA
Thanked: 25 times
Followed by:1 members
GMAT Score:750+

by VP_Tatiana » Fri May 09, 2008 7:54 am
The answer is B, 24:25. Here is how I got it.

We know the ratio of the rectangle's sides are 2:3. So, we can say that one side is 2x and one side is 3x, where x is some multiplicative factor that we don't know but don't need to know.

So, for the rectangle R we have:
P = 10x
A = 6x^2 (2x*3x)

Since the square has to have the same perimiter, for the square:
P = 10x (meaning each side is 5x/2)
A = (5x/2 squared)

So, the ratio of the area of rectangle to area of square is 6x^2 : (25x^2)/4. Dividing both sides by x^2, I get 6 : 25/4. Multiplying both sides by 4, I get 24:25.

As always, ask if you need more clarification. Best wishes,

Tatiana
Tatiana Becker | GMAT Instructor | Veritas Prep
Top
Master | Next Rank: 500 Posts
Posts: 446
Joined: Thu Jul 26, 2007 1:07 pm
Thanked: 6 times

by dferm » Fri May 09, 2008 8:10 am
Can you explain further how you are getting the perimeter of the square...?

This threw me off the loop..

Thanks.
Top
Master | Next Rank: 500 Posts
Posts: 446
Joined: Thu Jul 26, 2007 1:07 pm
Thanked: 6 times

by dferm » Fri May 09, 2008 8:19 am
I mean area of square
Top
Master | Next Rank: 500 Posts
Posts: 258
Joined: Thu Mar 29, 2007 3:15 am
Thanked: 7 times
Followed by:1 members

by anju » Fri May 09, 2008 12:00 pm
Another way to solve is by picking numbers. But you will have to be careful in picking numbers as you do not want to stuck in multiplication / division of complex numbers.

The ratio of a rectangle is 2:3. So the one side is 2x and the other side is 3x. Let's take x = 2. So now the sides are 4:3 (2*2 : 3*2).
with these numbers:
Perimeter of a rectangle = 2L + 2B = 2*4 + 2*6 = 8 + 12 = 20
Given: Perimeter of a rectangle = perimeter of a square which is equal to 20.
So length of a square = 20/4 = 5
Area of a Square = L * B = 5 * 5 = 25
Area of a Rectangle = L * B = 4 * 6 = 24

Ratio:- Area of a rectangle : Area of a Square = 24:25

Hope this helps..
Top
Post new topic Post Reply
• Page 1 of 1