If the area of a regular hexagon is equal to the area of an equilateral GMAT Problem Solving

Question: If the area of a regular hexagon is equal to the area of an equilateral triangle of side 12 cm, then the length, in cm, of each side of the hexagon is:
A. 4√6
B. 6√6
C. 2√6
D. √6
E. 3√6

Answer: C

Approach Solution (1):
The side of an equilateral triangle is 12 cm.
Let "a" be the side of the regular hexagon.
Now,
Area of regular hexagon =area of an equilateral triangle.
= 6*(√3/4)*a*a = (√3/4)*12*12
= a*a = 12*12/6
= a*a = 24
= a = 2√6
The length of each side ofhexagon is 2√6cm.
Correct option: C

Approach Solution (2):
Given that, the area of a regular hexagon is equal to the area of an equilateral triangle of side 12cm.
Let’s consider ‘a’ be the side of the regular hexagon.
6 x√3/4 x a x a= √3/4 x 12 x 12
a² = 24
a = 2√6
Correct option: C

Approach Solution (3):
Area of equilateral triangle with side a = 12
A = √3/4 x a x a
Area of a regular hexagon with side say h = 3 x √3/2 x h x h
From these two equations, we will get:
h = 2√6
Correct option: C

“If the area of a regular hexagon is equal to the area of an equilateral triangle of side 12 cm, then the length, in cm, of each side of the hexagon is:”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. 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.

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