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

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

This threw me off the loop..

Thanks.

I mean area of square

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..