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
We are given that the perimeters of square region S and rectangular region R are equal and that the sides of R are in the ratio 2 : 3. Let’s label the sides of our figures:
Width of rectangle R = 2x
Length of rectangle R = 3x
Side of square S = s
The perimeter of rectangular region R is 2(2x) + 2(3x) = 4x + 6x = 10x.
The perimeter of square region S is 4s.
Since the two perimeters are equal we can create the following equation:
4s = 10x
2s = 5x
s = (5/2)x
Lastly, we need to determine the areas of both rectangle R and square S.
Area of rectangle R = length * width
A = (3x)(2x) = 6x^2
Since s = (5/2)x, we can use (5/2)x for the side of S.
Area of square S = side^2
A = [(5/2)x]^2
A = (25x^2)/4
We must determine the ratio of the area of region R to the area of region S.
Area of R/Area of S
6x^2/[(25x^2)/4]
6/(25/4)
24/25
Alternate Solution:
We know the sides of the rectangle have a ratio of 2:3; thus we can express the sides of this rectangle as 2x and 3x for some number x. The perimeter of the rectangle, in terms of x, is then 3x + 2x + 3x + 2x = 10x. This is also the perimeter of the square, so taking x = 2 will give us easy numbers to work with.
When x = 2, the sides of the rectangle are 4 and 6; thus the area of the rectangle is 4 x 6 = 24.
Also, when x = 2, the perimeter of the square is 10x = 20; thus a side of the square will be 5. The area of the square will then be 5 x 5 = 25.
So, the ratio of the area of the rectangle to the area of the square is 24:25.
Answer: B
_________________
5-star rated online GMAT quant
self study course
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.