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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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New post 24 Sep 2017, 22:55
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  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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Re: if the side of an equilateral triangle decreased by 20% , its area is [#permalink]

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New post 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 = \(100 - 64 = 36%\)

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

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New post 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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