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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 ## If the perimeter of a rectangular property is 46 meters tagged by: VJesus12 ##### This topic has 3 expert replies and 0 member replies ## If the perimeter of a rectangular property is 46 meters If the perimeter of a rectangular property is 46 meters, and the area of the property is 76 square meters, what is the length of each of the shorter sides? A. 4 B. 6 C. 9 D. 18 E. 23 The OA is the option A. Experts, what are the equations I should use? Are 2X+2Y=46 and X*Y=76? I'd be thankful for your help. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Top Reply Hello vjesus12. Let's take a look at your question. You are correct, you have to use the formulas $$2X+2Y=46\ \ and\ \ \ \ \ X\cdot Y=76 .$$ Hence, $$X+Y=23\ \ and\ \ \ \ \ X=\frac{76}{Y}.$$ Replacing X on the first equation we get $$\frac{76}{Y}+Y=23\ \Leftrightarrow\ \ \ 76+Y^2=23Y\ \Leftrightarrow\ \ Y^2-23Y+76=0$$ $$Y^2-23Y+76=0\ \Leftrightarrow\ \ \left(Y-4\right)\left(Y-19\right)=0.$$ Hence, Y=4 or Y=19. If Y=4 then X+Y=23 implies that X=23-4=19. In this case, the dimensions of the rectangle are 4 and 19. If Y=19 then X+Y=23 implies that X=23-19=4. In this case, the dimensions of the rectangle are 4 and 19. In each case, the length of the shorter side is equal to 4. This is why the correct answer is the option A. I hope this answer can help you. Feel free to ask me again if you have a doubt. 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. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15387 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 VJesus12 wrote: If the perimeter of a rectangular property is 46 meters, and the area of the property is 76 square meters, what is the length of each of the shorter sides? A. 4 B. 6 C. 9 D. 18 E. 23 In any rectangle: A = LW. P = 2L + 2W. We can PLUG IN THE ANSWERS, which represent the value of W. Since LW = 76, the correct answer is almost certainly a factor of 76. Of the five answer choices, only A divides evenly into 76. When the correct answer is plugged in, P = 46. A: W=4 Since LW = 76, we get: (L)(4) = 76 L = 19. P = 2L + 2W = 2(19) + 2(4) = 38 + 8 = 46. Success! The correct answer is A. _________________ 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 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 VJesus12 wrote: If the perimeter of a rectangular property is 46 meters, and the area of the property is 76 square meters, what is the length of each of the shorter sides? A. 4 B. 6 C. 9 D. 18 E. 23 We can let W = the width and L = the length and create the equations: 2W + 2L = 46 W + L = 23 L = 23 - W and WL = 76 Substituting, we have: W(23 - W) = 76 23W - W^2 = 76 -W^2 + 23W - 76 = 0 W^2 - 23W + 76 = 0 (W - 4)(W - 19) = 0 W = 4 or W = 19 If W = 4, then L = 23 - 4 = 19. If W = 19, then L = 23 - 19 = 4. We see that the length of each of the shorter sides is 4. Answer:A _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder 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 • Award-winning private GMAT tutoring Register now and save up to$200

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