If the Side of an Equilateral Triangle Decreased by 20%, its Area is Decreased GMAT Problem Solving

Question: If the side of an equilateral triangle decreased by 20%, its area is decreased by what percent?

1. 36%
2. 40%
3. 60%
4. 64%
5. 70%

Correct Answer: A
Solution and Explanation:

Approach Solution 1:
Let the side of an equilateral triangle be a.
Area is √3/4∗a^2.
Now, the side becomes 0.8a,
New Area = √3/4∗(0.8a)^2= √3/4*0.64a^2
% change = new-old/old*100= 0.36*100 = 36%

Approach Solution 2:
With the use of formula for the area of an equilateral triangle: (a^2 x √3)/4, where a is the side. If the initial side is 10, then the original area is (10^2 x √3)/4 = 100√3/4 = 25√3.
Since the side decreased by 20%, the new side is 8, and the new area is (8^2 x √3)/4 = 64√3/4 = 16√3.

We use the percent change formula: (New - Old)/Old x 100. The percent change is:
(16√3 - 25√3)/25√3 x 100
-9√3/25√3 x 100
-9/25 x 100 = -36%, which is a 36% decrease.

Approach Solution 3:
Let the side be 100, Initial Area = 2500 root3
After reduction each side became 80
New area = 1600 root3
Difference between areas = 900 root3
900/2500 *100
Area was decreased by 36%

“If the side of an equilateral triangle decreased by 20%, its area is”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "The Official Guide for GMAT review".To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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