What Is The Circumference Of The Semicircle In The Figure Shown? GMAT Problem Solving

Question: What is the circumference of the semicircle in the figure shown?

1. 14π√6
2. 7π√6
3. 7π√6/ 2
4. 7π√6/ 3
5. 7π√6/ 4

“What is the circumference of the semicircle in the figure shown?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMATOfficial Guide 2020”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation

Approach Solution 1:

This question can be solved by only one approach.

Triangle 1:
The triangle on top is 30-60-90 triangle
So, we know the ratio of sides of the triangle is
x:x\(\sqrt{3}\):2x
From the triangle 1 on top, we know the side 2x=14, so x=7
Base of triangle 1 = 7\(\sqrt{3}\)
Triangle 2:
The triangle in the bottom is 45-45-90 triangle
So, we know the ratio of sides fof the triangle is x:x:x\(\sqrt{2}\)
The hypotenuse of the triangle with side is x\(\sqrt{2}\) = 7\(\sqrt{3}\)*\(\sqrt{2}\)
The hypotenuse of the triangle 2 = 7\(\sqrt{6}\)
Circle:
The hypotenuse of the triangle is the diameter of the circle.
Diameter = 7\(\sqrt{6}\)
Circumference = dπ = 7\(\sqrt{6}\)*π
Circumference of semicircle = (7\(\sqrt{6}\)*π)/2

Correct Answer: C

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