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# If the diagonal of rectangle Z is d, and the perimeter of

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If the diagonal of rectangle Z is d, and the perimeter of [#permalink]  03 Nov 2010, 15:10
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77% (02:31) correct 22% (01:51) wrong based on 89 sessions
If the diagonal of rectangle Z is d, and the perimeter of rectangle Z is p, what is the area of rectangle Z, in terms of d and p?

(A) (d^2 – p)/3
(B) (2d^2 – p)/2
(C) (p – d^2)/2
(D) (12d^2 – p^2)/8
(E) (p^2 – 4d^2)/8
[Reveal] Spoiler: OA

Last edited by Bunuel on 20 Jul 2012, 03:32, edited 1 time in total.
Edited the question and added the OA.
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Re: The Quest for 700: Weekly GMAT Challenge [#permalink]  03 Nov 2010, 15:17
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Expert's post
zisis wrote:
If the diagonal of rectangle Z is d, and the perimeter of rectangle Z is p, what is the area of rectangle Z, in terms of d and p?
(A) (d2 – p)/3
(B) (2d2 – p)/2
(C) (p – d2)/2
(D) (12d2 – p2)/8
(E) (p2 – 4d2)/8

NO OA - once provided i will update

IMO (A)

Let the sides of rectangle be x and y.

Given: d^2=x^2+y^2 and p=2(x+y). Question: area=xy=?

Square p --> p^2=4(x^2+2xy+y^2) --> substitute x^2+y^2 by d^2 --> p^2=4(d^2+2xy) --> p^2-4d^2=8xy --> area=xy=\frac{p^2-4d^2}{8}.

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Manager
Joined: 16 Feb 2010
Posts: 226
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Kudos [?]: 29 [0], given: 16

Re: The Quest for 700: Weekly GMAT Challenge [#permalink]  03 Nov 2010, 15:55
Bunuel wrote:
zisis wrote:
If the diagonal of rectangle Z is d, and the perimeter of rectangle Z is p, what is the area of rectangle Z, in terms of d and p?
(A) (d2 – p)/3
(B) (2d2 – p)/2
(C) (p – d2)/2
(D) (12d2 – p2)/8
(E) (p2 – 4d2)/8

NO OA - once provided i will update

IMO (A)

Let the sides of rectangle be x and y.

Given: d^2=x^2+y^2 and p=2(x+y). Question: area=xy=?

Square p --> p^2=4(x^2+2xy+y^2) --> substitute x^2+y^2 by d^2 --> p^2=4(d^2+2xy) --> p^2-4d^2=8xy --> area=xy=\frac{p^2-4d^2}{8}.

excellent explanation ! kudos
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Re: The Quest for 700: Weekly GMAT Challenge [#permalink]  03 Nov 2010, 18:47
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KUDOS
Expert's post
When answer is in terms of 1 or 2 variables, my suggestion would be to quickly take simple values. (If variables are more than that, keeping a track of their values becomes cumbersome)
I would say let the sides be 3 and 4 to get diagonal, d = 5 (Pythagorean triple). Then p = 2x3 + 2x4 = 14. You are looking for an area of 3x4 = 12
Put values and check.

There is a teeny-weeny chance that two options may give you the answer you are looking for. In that case, you might have to take different values and put in those two options to pick out the winner, but the risk is worth it, in my opinion.
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Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews Senior Manager Joined: 13 Aug 2012 Posts: 465 Concentration: Marketing, Finance GMAT 1: Q V0 GPA: 3.23 Followers: 14 Kudos [?]: 133 [0], given: 11 Re: If the diagonal of rectangle Z is d, and the perimeter of [#permalink] 12 Dec 2012, 20:11 Equation 1: d = \sqrt{L^2+W^2} Equation 2: p = 2(L+W) Combine 1 and 2: d^2 = L^2+W^2 p^2 = 4 ( L^2 + 2LW + W^2) p^2 = 4L^2 + 8LW + 4W^2 p^2 = 4d^2 + 8LW Remember that A = LW and \frac{p}{2}=L+W A = \frac{p^2-4d^2}{8} Answer: E _________________ Impossible is nothing to God. Last edited by mbaiseasy on 10 Jan 2013, 00:18, edited 1 time in total. Intern Joined: 20 Dec 2012 Posts: 2 Location: France Concentration: International Business, Strategy Schools: LBS '14 WE: Project Management (Telecommunications) Followers: 0 Kudos [?]: 5 [0], given: 3 Re: If the diagonal of rectangle Z is d, and the perimeter of [#permalink] 09 Jan 2013, 09:39 if we take a rectangle of 2x1 area A = 2x1 = 2 perimeter P = 2x2 + 2x1 = 6 the diagonal D = sqrt(1²+2²) = sqrt(5) for ansewer (B) (2d^2 – p)/2 (2D² - P) = 2*sqrt(5)² - 6 = 4 ==> 4/2 = 2 ==> which is the area A the same reasoning goes for answer E am i doing something wrong? because B and E are correct for me Manager Joined: 18 Oct 2011 Posts: 93 Location: United States Concentration: Entrepreneurship, Marketing GMAT Date: 01-30-2013 GPA: 3.3 Followers: 2 Kudos [?]: 15 [0], given: 0 Re: If the diagonal of rectangle Z is d, and the perimeter of [#permalink] 09 Jan 2013, 10:56 I just used real numbers to solve this question. Pick a rectangle with sides 3 and 4. Diagonal would be 5 so would = d. Perimeter = 14, Area = 12. Only E works. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 3732 Location: Pune, India Followers: 802 Kudos [?]: 3165 [0], given: 136 Re: If the diagonal of rectangle Z is d, and the perimeter of [#permalink] 09 Jan 2013, 19:58 Expert's post Cassiss wrote: if we take a rectangle of 2x1 area A = 2x1 = 2 perimeter P = 2x2 + 2x1 = 6 the diagonal D = sqrt(1²+2²) = sqrt(5) for ansewer (B) (2d^2 – p)/2 (2D² - P) = 2*sqrt(5)² - 6 = 4 ==> 4/2 = 2 ==> which is the area A the same reasoning goes for answer E am i doing something wrong? because B and E are correct for me When you take some numbers as you did here (say, distinct sides are 2 and 1 so p = 6, d = ...etc), it is possible that 2 or more options give you the correct answer. In that case, you need to take another set of numbers and put the values in only those two options. Hopefully, only one of them will give you the correct answer. Also, when picking numbers, try to pick those which need minimum effort. e.g. I would like to pick the sides as 3 and 4 because I know that the diagonal in that case will be 5. No messy square roots to handle. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
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Re: If the diagonal of rectangle Z is d, and the perimeter of   [#permalink] 09 Jan 2013, 19:58
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