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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 In quadrilateral ABCD above, what is the length of AB ? tagged by: AbeNeedsAnswers This topic has 2 expert replies and 1 member reply In quadrilateral ABCD above, what is the length of AB ? Timer 00:00 Your Answer A B C D E Global Stats Difficult In quadrilateral ABCD above, what is the length of AB ? A) âˆš26 B) 2âˆš5 C) 2âˆš6 D) 3âˆš2 E) 3âˆš3 C Source: Official Guide 2020 GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13040 messages Followed by: 1251 members Upvotes: 5254 GMAT Score: 770 AbeNeedsAnswers wrote: In quadrilateral ABCD above, what is the length of AB ? A) âˆš26 B) 2âˆš5 C) 2âˆš6 D) 3âˆš2 E) 3âˆš3 C Source: Official Guide 2020 [spoiler=][attachment=0]2019-04-26_1235.png[/attachment][/spoiler][/quote]First add a line to join B and D: If we focus on the blue right triangle, we can EITHER recognize that legs of length 3 and 4 are part of the 3-4-5 Pythagorean triplet, OR we can apply the Pythagorean Theorem. Either way, we'll see that the triangle's hypotenuse (BD) must have length 5 Now, when we focus on the red right triangle, we can . . . . . . apply the Pythagorean Theorem to write: xÂ² + 1Â² = 5Â² Simplify: xÂ² + 1 = 25 So: xÂ² = 24 So: x = âˆš24 = âˆš[(4)(6)] = (âˆš4)(âˆš6) = 2âˆš6 Answer: C 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! Top Member Legendary Member Joined 29 Oct 2017 Posted: 1013 messages Followed by: 4 members If we draw diagonal $$BD$$, weâ€™ve created two right triangles: $$BCD$$ and $$BAD$$. We see that triangle $$BCD$$ is a $$3-4-5$$ right triangle. So we see that side $$BD = 5$$. Therefore, triangle $$BAD$$ is a right triangle with a leg of $$1$$ and a hypotenuse of $$5$$. We can let side $$AB = n$$ and use the Pythagorean theorem to determine $$n$$. \begin{align*} 1^2 + n^2 &= 5^2\\ 1 + n^2 &= 25\\ n^2 &= 24\\ n &= \sqrt{24}\\ &= \sqrt{4} \cdot \sqrt{6} \\ &= 2\sqrt{6} \end{align*} GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 497 members Upvotes: 2867 GMAT Score: 800 Hi All, We're asked for the length of AB in quadrilateral ABCD. When dealing with 'weird' shapes, it often helps to break the shape down into 'pieces' that are easier to deal with. Here, if you draw a line from B to D, you will from 2 RIGHT TRIANGLES. Triangle BCD has legs of 3 and 4, so it's a 3/4/5 right triangle. Triangle BAD then has a leg of 1 and a hypotenuse of 5. We can use the Pythagorean Formula to find the missing leg... 1^2 + B^2 = 5^2 1 + B^2 = 25 B^2 = 24 From here, if we square-root both sides, we'll have... B = âˆš24 B = 2âˆš6 Final Answer: C GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to200

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