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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## What is the perimeter of Î" ABC ? tagged by: AAPL ##### This topic has 1 expert reply and 1 member reply ### Top Member ## What is the perimeter of Î" ABC ? Note: Figure not drawn to scale. In the figure above, ED = 1, CD = 2, and AE =6âˆš3. What is the perimeter of Î"ABC ? A. 3âˆš3 B. 10+5âˆš3 C. 10âˆš3 D. 15+5âˆš3 E. 25âˆš3 The OA is D. I need help with this PS question. Please, can any expert explain it for me? Thanks. Master | Next Rank: 500 Posts Joined 23 Jan 2009 Posted: 131 messages Followed by: 15 members Upvotes: 59 Hi AAPL, First thing to recognize is that triangles ABC and CDE are similar(Why?). Also, notice that triangle CED is a 30-60-90 triangle because short side is of length 1 and the hypotenuse is 2. That means CE= sqrt{3} and therefore AC= 5*sqrt{3} . From the ratios of sides in a 30-60-90 triangle, we obtain AB=5 and BC=10, and the perimeter of triangle ABC is equal to 15+5*sqrt{3} . Cheers, Dabral _________________ Free Video Explanations: 2018 OFFICIAL GUIDE FOR GMAT REVIEW. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Hello. Using the Pythagora's Theorem we can find CE. $$CE=\sqrt{2^2-1^2}=\sqrt{3}.$$ Now, AE=AC+CE, this implies that: $$AC=AE-CE=6\sqrt{3}-\sqrt{3}=5\sqrt{3}.$$ To calculate AB, we will use that triangles ABC and EDC are similar. So, $$\frac{AB}{ED}=\frac{AC}{CE},\ this\ implies\ that,\ \frac{AB}{1}=\frac{5\sqrt{3}}{\sqrt{3}},\ that\ is,\ AB=5.$$ Now, we can calculate BC using the Pythagora's Theorem again. We will get, $$BC=\sqrt{5^2+\ \left(5\sqrt{3}\right)^2}=\sqrt{25+75}=\sqrt{100}=10.$$ In conclusion, the perimeter of ABC is $$15+5\sqrt{3}.$$ The correct answer is D. I hope this can help you. Feel free to ask me again if you have any doubt. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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