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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 ## Triangle tagged by: Brent@GMATPrepNow ##### This topic has 3 expert replies and 0 member replies ## Triangle It took me a lot of time in calculations for this question. Is there a shorter way of doing it? Attachments This post contains an attachment. You must be logged in to download/view this file. Please login or register as a user. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15313 messages Followed by: 1863 members Upvotes: 13060 GMAT Score: 790 Quote: The perimeter of a certain isosceles right triangle is 16 + 16âˆš2. What is the length of the hypotenuse? a. 8 b. 16 c. 4âˆš2 d. 8âˆš2 e. 16âˆš2 The sides of an isosceles right triangle are in the following ratio: s : s : sâˆš2. Thus: If s=side and h=hypotenuse, then h = sâˆš2 and s = h/âˆš2. We can PLUG IN THE ANSWERS, which represent the length of the hypotenuse. Because h = sâˆš2, the average test-taker will assume that the correct answer must include âˆš2. Don't be an average test-taker. Start with an answer choice that does NOT include âˆš2. Answer choice B: h = 16 In this case: s = 16/âˆš2 = (16*âˆš2)/(âˆš2*âˆš2) = (16âˆš2)/2 = 8âˆš2. Thus: p = 8âˆš2 + 8âˆš2 + 16 = 16 + 16âˆš2. Success! The correct answer is B. _________________ 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 08 Dec 2008 Posted: 12922 messages Followed by: 1248 members Upvotes: 5254 GMAT Score: 770 Quote: The Perimeter of a certain isosceles right triangle is 16 + 16âˆš2. What is the length of the hypotenuse of the triangle? A) 8 B) 16 C) 4âˆš2 D) 8âˆš2 E) 16âˆš2 An IMPORTANT point to remember is that, in any isosceles right triangle, the sides have length x, x, and xâˆš2 for some positive value of x. Note: xâˆš2 is the length of the hypotenuse, so our goal is to find the value of xâˆš2 From here, we can see that the perimeter will be x + x + xâˆš2 In the question, the perimeter is 16 + 16âˆš2, so we can create the following equation: x + x + xâˆš2 = 16 + 16âˆš2, Simplify: 2x + xâˆš2 = 16 + 16âˆš2 IMPORTANT: Factor xâˆš2 from the left side to get : xâˆš2(âˆš2 + 1) = 16 + 16âˆš2 Now factor 16 from the right side to get: xâˆš2(âˆš2 + 1) = 16(1 + âˆš2) Divide both sides by (1 + âˆš2) to get: xâˆš2 = 16 Answer = B Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi eitijan, Here's a larger discussion on this question, including other ways to solve it and some noteworthy aspects about how the prompt is written: http://www.beatthegmat.com/hypotenuse-of-triangle-t276892.html GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com • FREE GMAT Exam Know how you'd score today for$0

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