A square piece of paper is cut into two rectangular pieces - A and B

Question

A square piece of paper is cut into two rectangular pieces - A and B, such that the area of A is twice that of B. What is the ratio of the perimeter of A to that of B ?

A. 5:4
B. 4:3
C. 3:2
D. 2:1
E. 3:1

Fresh GMAT Club Tests' Question

ShahadatHJ · Answer

Let the area of the square is 81.
Area A = 54 (9*6)
Area B = 27 (9*3)
Perimeter A = 2*(9+6) = 30
Perimeter B = 2*(9+3) = 24
A:B = 30:24 = 5:4

nidhihiremath · Answer

Is there any other way to solve this? How to decide which number to assume as the area.

ShahadatHJ · Answer

Since the total area was of a square, the numbers could be 1^2, 2^2. 3^2,....
I took 9^2 = 81 because we need a multiple of 3... And 81 is a multiple of 3. 
 nidhihiremath  you can try with 6^2 = 36 as well.

gmatophobia · Answer

Let's assume the side of the square = s

We are given that the area of A is twice that of B, hence the one side of A will be twice that of B. The other side of A and B will be equal.

Let's assume that side of A = a and the side of b = b

We know that  \frac{a}{b}  =  \frac{2}{1}

a = 2b

a + b = s

\frac{Perimeter (A) }{ Perimeter (B) }   =  \frac{2(s+a) }{ 2(s+b) }   =  \frac{(s+a) }{ (s+b) }

At this stage, we can assume the value of s in such a manner that its a multiple of 3.

Let's assume s = 6

a + b = 6

2b + b = 6

b = 2

a = 4

Let's substitute this information into the ratio -

\frac{Perimeter (A) }{ Perimeter (B) }   =  \frac{(s+a) }{ (s+b) }

=  \frac{(6+4) }{ (6+2) }

=  \frac{10 }{ 8 }

=  \frac{5 }{ 4}

Option A

LetsDoIt2022 · Answer

A pretty fast and straightforward way of getting to the solution is taking the unit square as we can just cut two opposing side lengths in the ratio to the areas given.  I can't yet upload images so here's a description.

So we cut it into:
- a rectangle with side lengths  \frac{1}{3}  and  1 , being the smaller rectangle (Rectangle  B )
- the other one will then be a rectangle with side lengths  \frac{2}{3}  and  1  (Rectangle  A  - with twice the area of rectangle  B )

Then we just add up the side lengths to get the perimeter of each rectangle:
Perimeter A = \frac{2}{3} + \frac{2}{3} + 1 + 1 = \frac{10}{3}  
Perimeter B = \frac{1}{3} + \frac{1}{3} + 1 + 1 = \frac{8}{3}

And get the ratio:
  \frac{Perimeter A}{Perimeter B}  =  \frac{10 * 3}{8 * 3}  =  \frac{10}{8}  =  \frac{5}{4}

vv65 · Answer

The figure below represents the square.

The x's and the y's are small squares of equal sizes. The x's together are the bigger rectangle and the y's together are the smaller rectangle.

x x x
x x x
y y y

Now just count.
Perimeter of the bigger square = 10
Perimeter of the smaller square = 8

Ratio = 10/8 = 5/4 = A

Posted from my mobile device

A square piece of paper is cut into two rectangular pieces - A and B

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A square piece of paper is cut into two rectangular pieces - A and B

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards