The Rectangles Shown Above Are Similar And The Ratio Of The Area Of GMAT Problem Solving

Question:

The rectangles shown above are similar and the ratio of the area of the small rectangle over the area of the big rectangle is ¼. What is the value of x?

(A) 24
(B) 36
(C) 48
(D) 72
(E) It cannot be determined from the information given

“The rectangles shown above are similar and the ratio of the area 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 number of qualitative skills. GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Solutions and Explanation

Approach Solution : 1

Finding the solution involves using proportionality between the two rectangles.
The sides of the larger rectangle have a 2:3 ratio. Similar to this, the smaller rectangle's sides should have a 2:3 ratio because 'x' is proportional to 144.

Now, x * y = 144 * 96/4

x∗2x/3 = 36*96

x*x = 3 * 36 * 96/2

X = √3*36*48
X = √3*6*6*4*4*3
X = 72

Correct Answer: (D)

Approach Solution : 2

The rectangles above are similar, and the ratio of the small rectangle's area to the big rectangle's area is ¼ , as well as the small rectangle's and big rectangle's lengths being ½ .
x/144 = ½

x = 72

Correct Answer: (D)

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