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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 ## A triangle of area 30 is formed by the line x/c + y/(c+7) - tagged by: fskilnik@GMATH ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## A triangle of area 30 is formed by the line x/c + y/(c+7) - ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult GMATH practice exercise (Quant Class 20) A triangle of area 30 is formed by the line x/c + y/(c+7) - 1 = 0 (where c is a positive constant) and the coordinate axes. What is the perimeter of this triangle? (A) 12 (B) 24 (C) 30 (D) 36 (E) 52 Answer: _____(C)__ _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15362 messages Followed by: 1866 members Upvotes: 13060 GMAT Score: 790 fskilnik@GMATH wrote: [size=17]GMATH practice exercise (Quant Class 20) A triangle of area 30 is formed by the line x/c + y/(c+7) - 1 = 0 (where c is a positive constant) and the coordinate axes. What is the perimeter of this triangle? (A) 12 (B) 24 (C) 30 (D) 36 (E) 52 Given that the area and the answer choices are all integers, the triangle is probably a Pythagorean Triple. The only Pythagorean Triple with an area of 30 is 5-12-13. In the given equation, test c=5, with the result that c+7 = 12: x/5 + y/12 - 1 = 0 If x=0, then y=12, implying a y-intercept at (0, 12). If y=0, then x=5, implying an x-intercept at (5, 0). Implication: In combination with the two axes, the line above will form a right triangle that has a height of 12 along the y-axis, a base of 5 along the x-axis, and a hypotenuse of 13, with the result that the area = (1/2)(12)(5) = 30. Perimeter = 5+12+13 = 30. The correct answer is C. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 fskilnik@GMATH wrote: GMATH practice exercise (Quant Class 20) A triangle of area 30 is formed by the line x/c + y/(c+7) - 1 = 0 (where c is a positive constant) and the coordinate axes. What is the perimeter of this triangle? (A) 12 (B) 24 (C) 30 (D) 36 (E) 52 Yes... 5-12-13 is an important GMAT Pythagorean Triple... $$?\,\, = \,\,\Delta \,\,{\rm{perimeter}}$$ $${S_\Delta } = 30\,\,\,\left( * \right)$$ $${x \over c} + {y \over {c + 7}} = 1\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{ \,x{\rm{ - intercept}} = c \hfill \cr \,y{\rm{ - intercept}} = c + 7 \hfill \cr} \right.\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,30 = {{c\left( {c + 7} \right)} \over 2}\,\,\,$$ $$c\left( {c + 7} \right) = 60\,\,\,\left[ { = 5 \cdot 12 = \left( { - 12} \right)\left( { - 5} \right)} \right]\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,c = 5\,\,\,{\rm{or}}\,\,\,c = - 12\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{stem}}} \,\,\,\,\,c = 5$$ $$\left\{ \matrix{ \,{\rm{right}}\,\,\Delta \hfill \cr \,{\rm{legs}}\,\,5,12 \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{hyp}}\,\, = 13\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,? = 5 + 12 + 13 = 30$$ The correct answer is (C). We follow the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep 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 • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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