ratio difference between a square and a rectangle

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