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# If a triangle ABC is there such that BE=EF=FC=3 and DB=GC=2BE, what is

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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If a triangle ABC is there such that BE=EF=FC=3 and DB=GC=2BE, what is  [#permalink]

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23 May 2016, 19:50
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35% (medium)

Question Stats:

83% (03:08) correct 17% (03:38) wrong based on 43 sessions

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If a triangle ABC is there such that BE=EF=FC=3 and DB=GC=2BE, what is the perimeter of a pentagon ADEFG?
A. 9+6√3
B. 6+4√3
C. 9+6√2
D. 6+4√2
E. 4+2√3

*An answer will be posted in 2 days.

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Status: Persevere Joined: 08 Jan 2016 Posts: 114 Location: Hong Kong GMAT 1: 750 Q50 V41 GPA: 3.52 Re: If a triangle ABC is there such that BE=EF=FC=3 and DB=GC=2BE, what is [#permalink] ### Show Tags 24 May 2016, 00:31 MathRevolution wrote: If a triangle ABC is there such that BE=EF=FC=3 and DB=GC=2BE, what is the perimeter of a pentagon ADEFG? A. 9+6√3 B. 6+4√3 C. 9+6√2 D. 6+4√2 E. 4+2√3 *An answer will be posted in 2 days. I could solve this question after assuming that DE and GF are perpendicular to side BC, making Triangles DBE and GFC right triangles. Since we know BE = 3 and BD = 6, we can calculate DE. DE = $$3\sqrt{3}$$. Similarly, GF = $$3\sqrt{3}$$. Now, the sides of Triangles DBE and GFC are in a ratio of $$1:\sqrt{3}:2$$. Hence, these are 30-60-90 triangles with angle DBE = angle GCF = 60. This implies that angle BAC =60 and Triangle ABC is an equilateral triangle. AB = BC = AC = 9 AD = AB - DB = 9 - 6 = 3 Similarly, AG = AC - GC = 9 - 6 = 3 So, perimeter of pentagon ADEFG = AD + AG + DE + GF + EF = $$3 + 3 + 3\sqrt{3} + 3\sqrt{3} + 3 = 9 + 6\sqrt{3}$$ Hence, the correct answer is A. However, the above solution is dependent on the assumption that DE and GF are perpendicular to BC. Probably, the question should provide this information either in the question stem or in the figure. Is there any way we can conclude that DE and GF are perpendicular to BC based on the given information ? Or are there any methods for calculating the perimeter without relying on the fact that DE and GF are perpendicular to BC? chetan2u - Can you help? Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8769 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If a triangle ABC is there such that BE=EF=FC=3 and DB=GC=2BE, what is [#permalink] ### Show Tags 25 May 2016, 17:21 Since BE=2 and DB=4, degree B = degree C=60 degree. So, DE=GF=3√3 and AD=AG=3. Hence, the perimeter of a pentagon ADEFG is 3+3+3+3√3+3√3=9+6√3.Hence,the correct answer is A. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: If a triangle ABC is there such that BE=EF=FC=3 and DB=GC=2BE, what is   [#permalink] 25 May 2016, 17:21
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