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If the side of an equilateral triangle decreased by 20%, its area is

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If the side of an equilateral triangle decreased by 20%, its area is  [#permalink]

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30 Jan 2019, 01:56
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If the side of an equilateral triangle decreased by 20%, its area is decreased by what percent?

A. 36%
B. 40%
C. 60%
D. 64%
E. 70%

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If the side of an equilateral triangle decreased by 20%, its area is  [#permalink]

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30 Jan 2019, 02:32
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Let the side of an equilateral triangle be a.
Area is $$\sqrt{3}/4*a^2$$.
Now, the side becomes 0.8a,
New Area = $$\sqrt{3}/4(0.8a)^2$$ = $$\sqrt{3}/4*0.64a^2$$

% change = $$\frac{New-Old}{Old}$$*100 = 0.36*100 = 36%

A is the answer.
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Re: If the side of an equilateral triangle decreased by 20%, its area is  [#permalink]

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30 Jan 2019, 02:55
Bunuel wrote:
If the side of an equilateral triangle decreased by 20%, its area is decreased by what percent?

A. 36%
B. 40%
C. 60%
D. 64%
E. 70%

let side be 10 and later 20% less 80
area with side 10 = 25 sqrt 3 and with side 8- 16 sqrt 3
so % decrease = 9 /25
36 %
IMO A
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Re: If the side of an equilateral triangle decreased by 20%, its area is  [#permalink]

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30 Jan 2019, 03:05
Bunuel wrote:
If the side of an equilateral triangle decreased by 20%, its area is decreased by what percent?

A. 36%
B. 40%
C. 60%
D. 64%
E. 70%

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%

IMO A

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Re: If the side of an equilateral triangle decreased by 20%, its area is  [#permalink]

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01 Feb 2019, 18:47
Bunuel wrote:
If the side of an equilateral triangle decreased by 20%, its area is decreased by what percent?

A. 36%
B. 40%
C. 60%
D. 64%
E. 70%

We use the 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.

Alternate solution:

We can use the fact that if a side of a regular polygon (equilateral triangle, square, regular pentagon, etc.) is increased or decreased such that the side’s new length is n times its original length, then the new area of the polygon is n^2 times its original area.

Since here the side of an equilateral triangle decreased by 20%, the side’s new length is 0.8 times its old length and thus the new area of the equilateral triangle is 0.8^2 = 0.64 times its original area, i.e., 64% of its original area. We see that this is a 36% decrease.

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Re: If the side of an equilateral triangle decreased by 20%, its area is   [#permalink] 01 Feb 2019, 18:47
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