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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 ## The area of an isoceles right triangle is... tagged by: BTGmoderatorLU ##### This topic has 1 expert reply and 0 member replies ### Top Member ## The area of an isoceles right triangle is... The area of an isoceles right triangle is $$18x^2+6x+\frac{1}{2}$$ Find the perimeter of the triangle. $$\left(A\right)\ \ 36x^2+12x+2$$ $$\left(B\right)\ \ 9x^2+3x+\frac{1}{4}$$ $$\left(C\right)\ \left(2+2^{\frac{1}{2}}\right)\left(6x+1\right)$$ $$\left(D\right)\ \left(1+2^{\frac{1}{2}}\right)\left(6x+1\right)$$ $$\left(E\right)18x+3$$ The OA is C. I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Hello LUANDATO. Let's take a look at you question. We have an isoceles right triangle with area: $$A=\ 18x^2+6x+\frac{1}{2}=\frac{1}{2}\cdot\left(36x^2+12x+1\right)=\frac{1}{2}\cdot\left(6x+1\right)\cdot\left(6x+1\right).$$ It implies that the length of two cathetus are: 6x+1. So, the lenght of the third side (hypotenuse) is: $$hip=\sqrt{\left(6x+1\right)^2+\left(6x+1\right)^2}=\sqrt{2\left(6x+1\right)^2}=\left(6x+1\right)\sqrt{2}=\left(6x+1\right)\cdot2^{\frac{1}{2}}.$$ Finally, the perimeter of the triangle is $$\left(6x+1\right)+\left(6x+1\right)+\left(6x+1\right)\cdot2^{\frac{1}{2}}=2\left(6x+1\right)+2^{\frac{1}{2}}\left(6x+1\right)=\left(2+2^{\frac{1}{2}}\right)\left(6x+1\right).$$ So, the correct answer is C. I hope this explanation may help you. I'm available if you'd like a follow up. Regards. _________________ 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 5-day free, full-access trial TTP Quant 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 GMAT Exam Know how you'd score today for$0

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