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Register now and save up to $200 Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE 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 Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code ## area tagged by: Brent@GMATPrepNow This topic has 8 expert replies and 3 member replies lukaswelker Senior | Next Rank: 100 Posts Joined 26 Mar 2014 Posted: 65 messages Followed by: 1 members #### area Thu Apr 17, 2014 8:42 am Elapsed Time: 00:00 • Lap #[LAPCOUNT] ([LAPTIME]) Hello guys I'm going to far in calculations and I get it wrong. There must be an easier way. Here goes the question, A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet? 19200 : 19600 : 20000 : 20400 : 20800. Please let me know if you see an easier way. Many thanks Lukas Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums! theCodeToGMAT Legendary Member Joined 14 Aug 2012 Posted: 1556 messages Followed by: 34 members Thanked: 448 times Target GMAT Score: 750 GMAT Score: 650 Thu Apr 17, 2014 9:14 am 560 = 2 * (L + B) L + B = 280 To find: L*B L^2 + B^2 = (200)^2 (L+B)^2 -2*L*B = 200^2 280^2 - 200^2 = 2 * L * B 480 * 80 = 2 * L * B L * B = 19200 _________________ R A H U L Thanked by: lukaswelker ### GMAT/MBA Expert Brent@GMATPrepNow GMAT Instructor Joined 08 Dec 2008 Posted: 10888 messages Followed by: 1215 members Thanked: 5211 times GMAT Score: 770 Thu Apr 17, 2014 9:26 am lukaswelker wrote: A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet? A) 19200 B) 19600 C) 20000 D) 20400 E) 20800. Let L and W equal the length and width of the rectangle respectively. perimeter = 560 So, L + L + W + W = 560 Simplify: 2L + 2W = 560 Divide both sides by 2 to get: L + W = 280 diagonal = 200 The diagonal divides the rectangle into two RIGHT TRIANGLES. Since we have right triangles, we can apply the Pythagorean Theorem. We get LÂ² + WÂ² = 200Â² NOTE: Our goal is to find the value of LW [since this equals the AREA of the rectangle] If we take L + W = 280 and square both sides we get (L + W)Â² = 280Â² If we expand this, we get: LÂ² + 2LW + WÂ² = 280Â² Notice that we have LÂ² + WÂ² "hiding" in this expression. That is, we get: LÂ² + 2LW + WÂ² = 280Â² We already know that LÂ² + WÂ² = 200Â², so, we'll take LÂ² + 2LW + WÂ² = 280Â² and replace LÂ² + WÂ² with 200Â² to get: 2LW + 200Â² = 280Â² So, 2LW = 280Â² - 200Â² Evaluate: 2LW = 38,400 Solve: LW = 19,200 = A For extra practice, here's a similar question: http://www.beatthegmat.com/area-of-a-rectangle-t100119.html Cheers, Brent _________________ Brent Hanneson â€“ Founder of GMATPrepNow.com Use our video course along with Check out the online reviews of our course Come see all of our free resources Thanked by: lukaswelker 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! osama_salah Newbie | Next Rank: 10 Posts Joined 15 Jun 2016 Posted: 8 messages Mon Jun 27, 2016 5:29 am How did you calculate 280Â² - 200Â² = 38,400 ? Brent@GMATPrepNow wrote: lukaswelker wrote: A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet? A) 19200 B) 19600 C) 20000 D) 20400 E) 20800. Let L and W equal the length and width of the rectangle respectively. perimeter = 560 So, L + L + W + W = 560 Simplify: 2L + 2W = 560 Divide both sides by 2 to get: L + W = 280 diagonal = 200 The diagonal divides the rectangle into two RIGHT TRIANGLES. Since we have right triangles, we can apply the Pythagorean Theorem. We get LÂ² + WÂ² = 200Â² NOTE: Our goal is to find the value of LW [since this equals the AREA of the rectangle] If we take L + W = 280 and square both sides we get (L + W)Â² = 280Â² If we expand this, we get: LÂ² + 2LW + WÂ² = 280Â² Notice that we have LÂ² + WÂ² "hiding" in this expression. That is, we get: LÂ² + 2LW + WÂ² = 280Â² We already know that LÂ² + WÂ² = 200Â², so, we'll take LÂ² + 2LW + WÂ² = 280Â² and replace LÂ² + WÂ² with 200Â² to get: 2LW + 200Â² = 280Â² So, 2LW = 280Â² - 200Â² Evaluate: 2LW = 38,400 Solve: LW = 19,200 = A For extra practice, here's a similar question: http://www.beatthegmat.com/area-of-a-rectangle-t100119.html Cheers, Brent ### GMAT/MBA Expert Brent@GMATPrepNow GMAT Instructor Joined 08 Dec 2008 Posted: 10888 messages Followed by: 1215 members Thanked: 5211 times GMAT Score: 770 Mon Jun 27, 2016 5:32 am osama_salah wrote: How did you calculate 280Â² - 200Â² = 38,400 ? Aside: 28Â² = 784, which means 280Â² = 78,400 So, 280Â² - 200Â² = 78,400 - 40,000 = 38,400 _________________ Brent Hanneson â€“ Founder of GMATPrepNow.com Use our video course along with Check out the online reviews of our course Come see all of our free resources Thanked by: osama_salah 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! setiavipul Newbie | Next Rank: 10 Posts Joined 06 Jun 2017 Posted: 1 messages Wed Jun 21, 2017 7:15 am Brent@GMATPrepNow wrote: lukaswelker wrote: A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet? A) 19200 B) 19600 C) 20000 D) 20400 E) 20800. Let L and W equal the length and width of the rectangle respectively. perimeter = 560 So, L + L + W + W = 560 Simplify: 2L + 2W = 560 Divide both sides by 2 to get: L + W = 280 diagonal = 200 The diagonal divides the rectangle into two RIGHT TRIANGLES. Since we have right triangles, we can apply the Pythagorean Theorem. We get LÂ² + WÂ² = 200Â² NOTE: Our goal is to find the value of LW [since this equals the AREA of the rectangle] If we take L + W = 280 and square both sides we get (L + W)Â² = 280Â² If we expand this, we get: LÂ² + 2LW + WÂ² = 280Â² Notice that we have LÂ² + WÂ² "hiding" in this expression. That is, we get: LÂ² + 2LW + WÂ² = 280Â² We already know that LÂ² + WÂ² = 200Â², so, we'll take LÂ² + 2LW + WÂ² = 280Â² and replace LÂ² + WÂ² with 200Â² to get: 2LW + 200Â² = 280Â² So, 2LW = 280Â² - 200Â² Evaluate: 2LW = 38,400 Solve: LW = 19,200 = A For extra practice, here's a similar question: http://www.beatthegmat.com/area-of-a-rectangle-t100119.html Cheers, Brent Why we can not use 45,45,90 degree property here? Diagonal of a rectangle divides two sides into 45 and 45 degree angle. Am i wrong here? ### GMAT/MBA Expert GMATGuruNY GMAT Instructor Joined 25 May 2010 Posted: 13499 messages Followed by: 1791 members Thanked: 12992 times GMAT Score: 790 Wed Jun 21, 2017 7:22 am Quote: A small rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet? a/ 19200 b/ 19600 c/ 20000 d/ 20400 e/ 20800 ALWAYS LOOK FOR SPECIAL TRIANGLES. Draw the rectangle and its diagonal: ttp://postimg.org/image/lglazede7/" target="_blank"> Since diagonal AD is a multiple of 5, check whether âˆ†ABD is a multiple of a 3:4:5 triangle. If each side of a 3:4:5 triangle is multiplied by 40, we get:: (40*3):(40*4):(40*5) = 120:160:200. The following figure is implied: ttp://postimg.org/image/wu9vjefp1/" target="_blank"> Check whether the resulting perimeter for rectangle ABCD is 560: 120+160+120+160 = 560. Success! Implication: For the perimeter of rectangle ABCD to be 560, âˆ†ABD must be a multiple of a 3:4:5 triangle with sides 120, 160 and 200. Thus: Area of rectangle ABCD = L * W = 160 * 120 = 19200. The correct answer is A. _________________ Mitch Hunt GMAT Private Tutor GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "Thank" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Thanked by: varunkhanna 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 Rich.C@EMPOWERgmat.com Elite Legendary Member Joined 23 Jun 2013 Posted: 8832 messages Followed by: 463 members Thanked: 2823 times GMAT Score: 800 Wed Jun 21, 2017 1:57 pm Hi All, It's important to remember that nothing about a GMAT question is ever 'random' - the wording and numbers/data are always carefully chosen. Thus, you can sometimes use the 'design' of a prompt to your advantage and spot the built-in patterns that are often there. Here, notice how ALL of the numbers are relatively 'nice', round numbers - even the diagonal is a nice number (and that doesn't happen very often when dealing with rectangles).... Since the answer choices are also round numbers, it's likely that the triangles that are 'hidden' in this rectangle are based on one of the common right-triangle patterns (in this case, the 3/4/5 - since 200 is a multiple of 5). Using that knowledge to our advantage, IF we had a 3/4/5 and the diagonal was 200, then that would be '40 times' 5... so the other two sides would be 40 times 4 and 40 times 3: 160 and 120. With those two side lengths, we'd have a perimeter of 2(160) + 2(120) = 560... and that is an exact MATCH for what we were told, so this MUST be the situation that we're dealing with. At this point, the area can be calculated easily enough: (L)(W) = (160)(120) = 19,200 Final Answer: A GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert Brent@GMATPrepNow GMAT Instructor Joined 08 Dec 2008 Posted: 10888 messages Followed by: 1215 members Thanked: 5211 times GMAT Score: 770 Thu Jun 22, 2017 5:09 am setiavipul wrote: Why we can not use 45,45,90 degree property here? Diagonal of a rectangle divides two sides into 45 and 45 degree angle. Am i wrong here? That rule doesn't apply to rectangles. It does, however apply to squares Cheers, Brent _________________ Brent Hanneson â€“ Founder of GMATPrepNow.com Use our video course along with Check out the online reviews of our course Come see all of our 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 DavidG@VeritasPrep Legendary Member Joined 14 Jan 2015 Posted: 2380 messages Followed by: 115 members Thanked: 1121 times GMAT Score: 770 Thu Jun 22, 2017 8:41 am Quote: Why we can not use 45,45,90 degree property here? Diagonal of a rectangle divides two sides into 45 and 45 degree angle. Am i wrong here? Note also, that if the figure were a square, and the perimeter were 560, each side would be 560/4 = 140. If each side of a 45/45/90 triangle were 140, the hypotenuse, or diagonal, would be 140 *rt2. So the fact that the diagonal is 200 tells us that we're not dealing with a square (or 45:45:90 triangles.) _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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Thu Jun 22, 2017 8:44 am
DavidG@VeritasPrep wrote:
Quote:
Why we can not use 45,45,90 degree property here? Diagonal of a rectangle divides two sides into 45 and 45 degree angle. Am i wrong here?
Note also, that if the figure were a square, and the perimeter were 560, each side would be 560/4 = 140. If each side of a 45/45/90 triangle were 140, the hypotenuse, or diagonal, would be 140 *rt2. So the fact that the diagonal is 200 tells us that we're not dealing with a square (or 45:45:90 triangles.)
One more fun note. For a set perimeter, the rectangle with the greatest area is a square. If the shape in question had been a square, and the sides had each been 140, the area would have been 140*140 = 19,600. Because we know the shape is not a square, we know the area would be less than 19,600. The answer must be A

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Thu Jun 22, 2017 4:50 pm
DavidG@VeritasPrep wrote:
DavidG@VeritasPrep wrote:
Quote:
Why we can not use 45,45,90 degree property here? Diagonal of a rectangle divides two sides into 45 and 45 degree angle. Am i wrong here?
Note also, that if the figure were a square, and the perimeter were 560, each side would be 560/4 = 140. If each side of a 45/45/90 triangle were 140, the hypotenuse, or diagonal, would be 140 *rt2. So the fact that the diagonal is 200 tells us that we're not dealing with a square (or 45:45:90 triangles.)
One more fun note. For a set perimeter, the rectangle with the greatest area is a square. If the shape in question had been a square, and the sides had each been 140, the area would have been 140*140 = 19,600. Because we know the shape is not a square, we know the area would be less than 19,600. The answer must be A
I love that, nice hack!

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