GMAT Prep ?? (Geometry)

dferm · Posted: Fri May 09, 2008 7:48 am Post subject: GMAT Prep ?? (Geometry)

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...

VP_Tatiana · Posted: Fri May 09, 2008 8:54 am Post subject:

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

dferm · Posted: Fri May 09, 2008 9:10 am Post subject:

Can you explain further how you are getting the perimeter of the square...?

This threw me off the loop..

Thanks.

dferm · Posted: Fri May 09, 2008 9:19 am Post subject:

I mean area of square

anju · Posted: Fri May 09, 2008 1:00 pm Post subject:

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..