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

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Manager
Joined: 07 Jun 2017
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Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
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WE: Information Technology (Computer Software)
if the side of an equilateral triangle decreased by 20% , its area is [#permalink]

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24 Sep 2017, 22:55
00:00

Difficulty:

35% (medium)

Question Stats:

64% (00:21) correct 36% (00:44) wrong based on 11 sessions

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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%
[Reveal] Spoiler: OA

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Kudos [?]: 85 [0], given: 59

Manager
Joined: 12 Jun 2016
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Location: India
WE: Sales (Telecommunications)
Re: if the side of an equilateral triangle decreased by 20% , its area is [#permalink]

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25 Sep 2017, 04:08
If each side of a Equilateral triangle is reduced by same percent, the new triangle will still be equilateral. Meaning old and new Triangle are similar.

Let old side = 100. New side = 80

$$\frac{New}{Old} = \frac{80}{100} = \frac{4}{5}$$

$$\frac{New \ Area}{Old \ Area} = (\frac{4}{5})^2 = (\frac{16}{25}) = \frac{64}{100}$$

Therefore percentage decrease = $$100 - 64 = 36%$$

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

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25 Sep 2017, 04:23
Formula used:
Area of an equilateral triangle = $$\frac{sqrt(3)}{4}*side^2$$

Let the side of the triangle be 1
The side of the new triangle reduces by 20%(becomes $$0.8 = \frac{4}{5}$$)

If the area of the first triangle is $$\frac{sqrt(3)}{4}*1^2$$,
the are of the second triangle is $$\frac{sqrt(3)}{4}*\frac{16}{25}$$

Therefore the ratio of the two triangles is $$\frac{25}{16}$$

The difference is $$25-16 = 9$$ and the resulting percentage is $$\frac{9}{25}*100 = 36%$$(Option A)
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if the side of an equilateral triangle decreased by 20% , its area is   [#permalink] 25 Sep 2017, 04:23
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