If the perimeter of square region s and the perimeter of rectangular region r are equal and the sides of r are in the ratio 2: 3 then the ratio of the area of r to the area of s
a. 25: 16
b. 24: 25
c. 5: 6
d. 4: 5
e. 4: 9

 The correct option is (B) 24 : 25.

Step-by-step explanation:  Given that the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2 : 3.

We are to find the ratio of the area of R to the area of S.

Let 2x, 3x be the sides of rectangle R and y be the side of square S.

Then, according to the given information, we have

Therefore, the ratio of the area of R to the area of S is

Thus, the required ratio of the area of R to the area of S is 24 : 25.

Option (B) is CORRECT.

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