If The Area Of A Rectangle Is Equal To The Area Of A Square, Then The GMAT Problem Solving

Question: If the area of a rectangle is equal to the area of a square, then the perimeter of the rectangle must be

(A) one half of the perimeter of the square
(B) equal to the perimeter of the square
(C) equal to twice the perimeter of the square
(D) equal to the square root of the perimeter of the square
(E) none of the above

“If the area of a rectangle is equal to the area of a square, then the''- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT quant section tests the level of intelligence and calculative literacy of the students. The students must pick the correct answer choice by solving the entire sum logically and mathematically. The students must know basic mathematics like arithmetic, algebra and geometry to crack GMAT Problem Solving questions. The calculative problems of the GMAT Quant topic in the problem-solving part can only be solved with better skills in mathematics.

Solution and Explanation:

Approach Solution 1:

The problem statement informs that:

Given:

• area of a rectangle is equal to the area of a square.

Find Out:

• the perimeter of the rectangle.

Since the area of rectangle= area of square, then we can say,
Length x breadth (lb) = side (s) x side (s)
As per the formula, the perimeter of the square= 4 x side = 4s = 4 √lb
According to the formula of the rectangle, the perimeter of the rectangle = 2 (length + breadth)
That can be written as 2l + 2b. This cannot be described or written in terms of the perimeter of the square.

Correct Answer: (E)

Approach Solution 2:

The problem statement implies that:

Given:

• area of a rectangle is equal to the area of a square.

Find Out:

• the perimeter of the rectangle.

Let’s assume the dimensions of the rectangle are 8 and 2 and the side of the square is 4.
As per the question, the area of the rectangle= area of the square, which is equal to the product of the dimensions = 16
The perimeter of the rectangle = 2(l+b) (as per the formula of rectangle)
The perimeter of the rectangle is 2(2 + 8) = 20
On the other hand, the perimeter of the square is = 4*side (according to the formula of the square)
Therefore, the perimeter of the square= 4* 4= 16

Thus it can be analysed none of the answer choices from A to D is correct.

Correct Answer: (E)

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