Question: 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

1. 25:16
2. 24:25
3. 5:6
4. 4:5
5. 4:9

Correct Answer: B
Solution and Explanation:
Approach Solution 1:
Let the side of square be s and the side of rectangle a and b

Given:

The sides of R are in the ratio 2:3 --> a/b= 2/3--> b= 3a/2.
The perimeter of square region S and the perimeter of rectangular region R are equal --> P= 4s= 2(a+b) --> 2s= a+b= 5a/2 --> s=5a/4.

Question: area of R/area of S= ab/s^2= ?

Substitute b = 3a/2 and s= 5a/4 into the question: ab/s^2= 3a^2/2∗16/25a^2= 24/25.
= 24:25

Approach Solution 2:
In figure R –
Length = 3 ; Breadth = 2
Area of R = 6 and Perimeter of R = 2 ( 3 + 2 ) => 10
In figure S –
Sides = S (Say)
So, 4s = 10
Or, s = 5/2
Area of S = 25/4

Hence area of R to the area of S = 6 : 25/4 => 24 : 25

Approach Solution 3:
We know Perimeter of a square (Ps)= 4*side
Perimeter of a rectangle (Pr)= 2(length+breadth)

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

“If the perimeter of square region S and the perimeter of”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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