Question: The area of an equilateral triangle with side length x is the same as the surface area of a cube with edge length z. what is x^2 in terms of z^2 ?

1. Z^2 (6√3)
2. Z^2 (8√3)
3. 72 Z^2
4. Z^2 (72√3)
5. 192 Z^2

Correct Answer: (B)

Approach Solution : 1

Let x be the area of an equilateral triangle.
So, Area of equilateral triangle = (√3/4)∗x^2
Let z be the side of a cube.
Total surface area of a cube = 6∗(z^2)
The question clearly states that the area of the equilateral triangle = total surface area of the cube.
So we can write,
=> (√3/4)∗x^2 = 6∗(z^2)
Now multiply and divide the fraction by √3
=> x^2 = [6∗4∗√3∗(z^2)] / (√3∗√3)
=> x^2 = [6∗4∗√3∗(z^2)] / 3 = 8∗√3∗(z^2)
Therefore x^2 (8√3) is x^2 in terms of z^2.
This question has only one approach available.

“The area of an equilateral triangle with side length x is the same” - is a subject covered in the GMAT quantitative reasoning section. A student needs to be knowledgeable in a wide range of qualitative skills in order to successfully complete GMAT Problem Solving questions. There are 31 questions in the GMAT Quant section overall. Calculative mathematical problems must be solved in the GMAT quant topics' problem-solving section using appropriate mathematical skills.

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