manalq8 wrote:

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

help needed please

We know Perimeter of a square (Ps) = 4*side

Perimeter of a rectangle (Pr) = 2(length+breath)

Let us assume 40 to be the perimeter of the square (since we know each side of a square is equal and the perimeter is divisible by 4, also take in to account the length and breadth of the rectangle is in the ration 2k:3k = 5k; we can assume such a number)

Therefore,

Ps = Pr = 40

Area of the square = 100 sq. units

We know 2(length+breadth) = 40

i.e. length + breadth = 20 (or 5k = 20 given that l:b (or b:l) = 2:3)

Therefore length = 8, breath = 12

Area of the rectangle = 8*12 = 96 sq. units

Question asked = Area of the rectangle : Area of the square = 96:100 ==> 24:25

Note : The explanation might be bigger, but it takes less than 15 seconds to solve this problem if you assume numbers and try the problem.