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In the given figure, the area of the equilateral triangle is

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In the given figure, the area of the equilateral triangle is [#permalink]

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In the given figure, the area of the equilateral triangle is 48. If the other three figures are squares, what is the perimeter, approximately, of the nine-sided shape they form?

A) \(8\sqrt{2}\)
B) \(24\sqrt{3}\)
C) \(72\sqrt{2}\)
D) \(144\sqrt{2}\)
E) \(384\)
[Reveal] Spoiler: OA

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Last edited by Bunuel on 15 Sep 2013, 12:31, edited 3 times in total.
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In the given figure, the area of the equilateral triangle is 48. If the other three figures are squares, what is the perimeter, approximately, of the nine-sided shape they form?

A) \(8\sqrt{2}\)
B) \(24\sqrt{3}\)
C) \(72\sqrt{2}\)
D) \(144\sqrt{2}\)
E) \(384\)

The area of equilateral triangle is \(side^2*\frac{\sqrt{3}}{4}\).

So, we are given that \(side^2*\frac{\sqrt{3}}{4}=48\) --> \(side^2=64\sqrt{3}\) --> \(side=8\sqrt[4]{3}\).

The perimeter = \(9*8\sqrt[4]{3}=72\sqrt[4]{3}\) --> \(\sqrt[4]{3}\approx{\sqrt{2}}\).

Answer: C.
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Re: In the given figure, the area of the equilateral triangle is [#permalink]

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New post 19 Nov 2013, 22:18
Buneul, how did you estimate \(fourth\sqrt{3}\)=\(\sqrt{2}\)?
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New post 13 Feb 2014, 03:49
Hi Bunuel the question is really how can we understand the value of \(3^{1/4} = \sqrt{2}\) ??

I was stuck at this point as well. How does \(9*8*(3)^{1/4}\) convert to \(9*8*\sqrt{2}\) It may be something very small but I am not able to wrap my head around it.

Bunuel wrote:
madn800 wrote:
Buneul, how did you estimate \(fourth\sqrt{3}\)=\(\sqrt{2}\)?


\(side^2=64\sqrt{3}\) --> \(side^2=8^2*\sqrt{3}\) --> \(side=\sqrt{8^2*\sqrt{3}}\)--> \(side=8\sqrt[4]{3}\).

Hope it's clear.

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Re: In the given figure, the area of the equilateral triangle is [#permalink]

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New post 13 Feb 2014, 06:50
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gmatprav wrote:
Hi Bunuel the question is really how can we understand the value of \(3^{1/4} = \sqrt{2}\) ??

I was stuck at this point as well. How does \(9*8*(3)^{1/4}\) convert to \(9*8*\sqrt{2}\) It may be something very small but I am not able to wrap my head around it.

Bunuel wrote:
madn800 wrote:
Buneul, how did you estimate \(fourth\sqrt{3}\)=\(\sqrt{2}\)?


\(side^2=64\sqrt{3}\) --> \(side^2=8^2*\sqrt{3}\) --> \(side=\sqrt{8^2*\sqrt{3}}\)--> \(side=8\sqrt[4]{3}\).

Hope it's clear.


The trick here is that any positive integer root from a number more than 1 will be more than 1. For example: \(\sqrt[1000]{2}>1\).

So, we know that \(1<\sqrt[3]{3}<2\). We also know that \(\sqrt{2}\approx {1.4}\). So, \(1<(\sqrt[4]{3}\approx{\sqrt{2}})<2\).

Does this make sense?
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Re: In the given figure, the area of the equilateral triangle is [#permalink]

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New post 13 Feb 2014, 09:35
Thanks Bunuel, that makes sense now, coupled with the fact that the question is asking for approximate value not exact value. Thanks!!
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Re: In the given figure, the area of the equilateral triangle is   [#permalink] 10 Jul 2015, 05:03
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