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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] New post 15 Sep 2013, 09:08
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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, 11:31, edited 3 times in total.
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Re: In the given figure, the area of the equilateral triangle is [#permalink] New post 15 Sep 2013, 11:29
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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] New post 19 Nov 2013, 21:18
Buneul, how did you estimate fourth\sqrt{3}=\sqrt{2}?
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Re: In the given figure, the area of the equilateral triangle is [#permalink] New post 20 Nov 2013, 01:28
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Re: In the given figure, the area of the equilateral triangle is [#permalink] New post 13 Feb 2014, 02:49
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] New post 13 Feb 2014, 05:50
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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] New post 13 Feb 2014, 08:35
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] New post 13 Feb 2014, 09:12
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gmatprav wrote:
Thanks Bunuel, that makes sense now, coupled with the fact that the question is asking for approximate value not exact value. Thanks!!


Yes, the fact that we need only the approximate value is the key here.
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: In the given figure, the area of the equilateral triangle is   [#permalink] 13 Feb 2014, 09:12
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