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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 a certain right triangle? tagged by: AAPL ##### This topic has 1 expert reply and 1 member reply ### Top Member ## What is the perimeter of a certain right triangle? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult What is the perimeter of a certain right triangle? (1) The hypotenuse's length is 10 (2) The triangle's area is 24 The OA C. The trick with this question is that in statement 1 we cannot actually assume that the sides are 6 and 8 just because we know that x^2 +y^2 = 100 We cannot make any assumptions about X and Y UNLESS there is a restriction such as "X and Y must be integers" or "The product of XY is 48." Hence, the correct answer is C. Has anyone another strategic approach to solving this DS question? Regards! ### Top Member Legendary Member Joined 02 Mar 2018 Posted: 826 messages Followed by: 1 members Perimeter of a triangle = Side a + Side b + Side c However, if we have 2 known sides we can find the third side with Pythagoras theories before calculating the perimeter. Statement 1 = The hypotenuse length is 10 Given that hypotenuse = 10 Let opposite and adjacent be a and b respectively. From Pythagoras theories; we have $$10^2\ =\ a^2\ +\ b^2$$ $$100\ =\ a^2\ +\ b^2$$ The given information is not enough to find the perimeter of the triangle, hence statement 1 is INSUFFICIENT. Statement 2 = The triangle's are is 24 $$Area\ of\ triangle\ =\ \frac{1}{2}\ \cdot\ base\ \cdot\ height.$$ $$=\ \frac{1}{2}\ \cdot\ opposite\ \cdot\ adjacent.$$ $$=\ \frac{1}{2}\ \cdot\ a\ \cdot\ b.$$ $$24=\ \frac{1}{2}\ \cdot\ a\ \cdot\ b.$$ $$24=\ \frac{ab}{2}$$ $$ab\ =\ 48$$ This does not provide us with information on any of the sides, hence Statement 2 is INSUFFICIENT. Combining Statement 1 and 2 together = $$a^2\ +\ b^2\ =100\ -\ Statement\ 1$$ $$ab=48\ -\ Statement\ 2$$ From Statement 1 $$a^2\ +\ b^2\ =\ 100$$ $$a^2\ +\ b^2\ can\ bw\ written\ as\ \left(a\ +\ b\right)^2$$ $$\left(a\ +\ b\right)^2\ =\ \left(a\ +\ b\right)\cdot\left(a\ +\ b\right)$$ $$=\left(a\ \cdot\ a\right)\ +\left(a\ \cdot b\right)+\left(b\ \cdot\ a\right)+\ \left(b\cdot b\right)$$ $$=a^2\ +\ b^2\ +\ 2ab$$ $$From\ Statement\ 1\ a^2\ +\ b^2\ =100$$ $$From\ Statement\ 2\ \ ab=\ 48$$ $$\left(a\ +\ b\right)^2\ =\ \left(a^{2\ }+b^2\right)+\ \left(2ab\right)$$ $$=\ \left(100\right)\ +\ \left(2\ \cdot\ 48\right)$$ $$=\ 100\ +\ 96$$ $$=196$$ $$\sqrt{\left(a\ +\ b\right)^2}=\sqrt{196}$$ $$a\ +\ b\ =\ 14$$ We already have hypotenuse as 10 Opposite and adjacent as a + b = 14 Perimeter = (a + b ) + 10 =14 + 10 = 24 Option C is CORRECT. ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1273 messages Followed by: 29 members Upvotes: 59 AAPL wrote: What is the perimeter of a certain right triangle? (1) The hypotenuse's length is 10 (2) The triangle's area is 24 Has anyone another strategic approach to solving this DS question? Regards! Sure! The key point is to understand we are looking for the uniqueness (or not) of numerical values, not explicit calculations! (Our method has this important detail in its "backbone" when dealing with ANY Data Sufficiency problem... especially in Geometry-related ones!) $right\,\,\Delta \,\,\,:\,\,\,a \leqslant b < c\,\,\,{\text{sides}}\,\,\,\,\,$ $?\,\, = \,\,{\text{peri}}{{\text{m}}_{\,\Delta }}$ $\left( 1 \right)\,\,\,{\text{c}} = 10\,\,\,\,\,::\,\,\,\,{\text{GEOMETRIC}}\,\,{\text{BIFURCATION}}\,\,\,\,\,\,\left( {{\text{see}}\,\,{\text{image}}\,\,{\text{attached}}} \right)\,\,$ $\left( 2 \right)\,\,\,{S_\Delta } = 24\,\,\,\left\{ \begin{gathered} \,\left( {a,b,c} \right) = \left( {3 \cdot 2\,\,,4 \cdot 2\,\,,\,\,5 \cdot 2} \right)\,\,\,\,\,\,\left[ {3k,4k,5k} \right]\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,?\,\,\, = \,\,\,2\left( {3 + 4 + 5} \right) = 24 \hfill \\ \,\left( {a,b,c} \right) = \left( {\sqrt {2 \cdot 24} \,\,,\sqrt {2 \cdot 24} \,\,,\,\,\sqrt {2 \cdot 24} \, \cdot \sqrt 2 } \right)\,\,\,\,\,\,\,\,\,\left[ {L,L,L\sqrt 2 } \right]\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,?\,\,\, \ne \,\,24 \hfill \\ \end{gathered} \right.$ $\left( {1 + 2} \right)\,\,24 = \frac{{10 \cdot h}}{2}\,\,\,\,\, \Rightarrow \,\,\,\,h\,\,\,{\text{unique}}\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {{\text{see}}\,\,{\text{image}}\,\,{\text{attached}}} \right)} \,\,\,\,\Delta \,\,\,unique\,\,\,\left( {{\text{but}}\,\,{\text{congruents!}}} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,?\,\, = \,\,{\text{peri}}{{\text{m}}_{\,\Delta }}\,\,\,{\text{unique}}$ This solution follows 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 • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE 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 • 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 • FREE GMAT Exam Know how you'd score today for$0

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