It is currently 21 Nov 2017, 05:26

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

3 KUDOS received
Manager
Manager
avatar
Joined: 16 Feb 2010
Posts: 218

Kudos [?]: 378 [3], given: 16

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

Show Tags

New post 03 Nov 2010, 16:10
3
This post received
KUDOS
9
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

73% (02:08) correct 27% (02:24) wrong based on 630 sessions

HideShow timer Statistics

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, 04:32, edited 1 time in total.
Edited the question and added the OA.

Kudos [?]: 378 [3], given: 16

Expert Post
7 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42280

Kudos [?]: 132894 [7], given: 12391

Re: The Quest for 700: Weekly GMAT Challenge [#permalink]

Show Tags

New post 03 Nov 2010, 16:17
7
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
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 \(d^2\) --> \(p^2=4(d^2+2xy)\) --> \(p^2-4d^2=8xy\) --> \(area=xy=\frac{p^2-4d^2}{8}\).

Answer: E.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132894 [7], given: 12391

Manager
Manager
avatar
Joined: 16 Feb 2010
Posts: 218

Kudos [?]: 378 [0], given: 16

Re: The Quest for 700: Weekly GMAT Challenge [#permalink]

Show Tags

New post 03 Nov 2010, 16:55
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 \(d^2\) --> \(p^2=4(d^2+2xy)\) --> \(p^2-4d^2=8xy\) --> \(area=xy=\frac{p^2-4d^2}{8}\).

Answer: E.


excellent explanation ! kudos

Kudos [?]: 378 [0], given: 16

Expert Post
3 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7741

Kudos [?]: 17830 [3], given: 235

Location: Pune, India
Re: The Quest for 700: Weekly GMAT Challenge [#permalink]

Show Tags

New post 03 Nov 2010, 19:47
3
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
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.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17830 [3], given: 235

Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 458

Kudos [?]: 558 [0], given: 11

Concentration: Marketing, Finance
GPA: 3.23
GMAT ToolKit User
Re: If the diagonal of rectangle Z is d, and the perimeter of [#permalink]

Show Tags

New post 12 Dec 2012, 21:11
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, 01:18, edited 1 time in total.

Kudos [?]: 558 [0], given: 11

Intern
Intern
avatar
Joined: 20 Dec 2012
Posts: 2

Kudos [?]: 7 [0], given: 3

Location: France
Concentration: International Business, Strategy
Schools: LBS '14
WE: Project Management (Telecommunications)
Re: If the diagonal of rectangle Z is d, and the perimeter of [#permalink]

Show Tags

New post 09 Jan 2013, 10:39
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

Kudos [?]: 7 [0], given: 3

Manager
Manager
avatar
Joined: 18 Oct 2011
Posts: 89

Kudos [?]: 91 [0], given: 0

Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
Re: If the diagonal of rectangle Z is d, and the perimeter of [#permalink]

Show Tags

New post 09 Jan 2013, 11:56
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.

Kudos [?]: 91 [0], given: 0

Expert Post
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7741

Kudos [?]: 17830 [0], given: 235

Location: Pune, India
Re: If the diagonal of rectangle Z is d, and the perimeter of [#permalink]

Show Tags

New post 09 Jan 2013, 20:58
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

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17830 [0], given: 235

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15582

Kudos [?]: 283 [0], given: 0

Premium Member
Re: If the diagonal of rectangle Z is d, and the perimeter of [#permalink]

Show Tags

New post 15 Jul 2014, 13:54
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 283 [0], given: 0

1 KUDOS received
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1851

Kudos [?]: 2717 [1], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If the diagonal of rectangle Z is d, and the perimeter of [#permalink]

Show Tags

New post 15 Jul 2014, 22:20
1
This post received
KUDOS
Refer diagram below:

Let one side of the rectangle = a

Other side \(= \frac{p}{2} - a\)

Require to find \(Area = a (\frac{p}{2} - a) = \frac{ap}{2} - a^2\)

\(d^2 = a^2 + (\frac{p}{2} - a)^2\)

\(d^2 = 2a^2 + \frac{p^2}{4} - ap\)

\(ap - 2a^2 = \frac{p^2}{4} - d^2\)

\(\frac{ap}{2} - a^2 = \frac{p^2 - 4d^2}{8}\)

Answer = E
Attachments

rec.png
rec.png [ 3.79 KiB | Viewed 5093 times ]


_________________

Kindly press "+1 Kudos" to appreciate :)

Kudos [?]: 2717 [1], given: 193

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15582

Kudos [?]: 283 [0], given: 0

Premium Member
Re: If the diagonal of rectangle Z is d, and the perimeter of [#permalink]

Show Tags

New post 24 Jul 2015, 13:42
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 283 [0], given: 0

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15582

Kudos [?]: 283 [0], given: 0

Premium Member
Re: If the diagonal of rectangle Z is d, and the perimeter of [#permalink]

Show Tags

New post 25 Jul 2016, 08:21
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 283 [0], given: 0

Senior Manager
Senior Manager
avatar
Joined: 02 Mar 2012
Posts: 360

Kudos [?]: 91 [0], given: 4

Schools: Schulich '16
Re: If the diagonal of rectangle Z is d, and the perimeter of [#permalink]

Show Tags

New post 26 Jul 2016, 01:55
the question rotating on the formula:
(x+y)^2=x^2+y^2+2xy

just solve acc and get answer E

Kudos [?]: 91 [0], given: 4

Re: If the diagonal of rectangle Z is d, and the perimeter of   [#permalink] 26 Jul 2016, 01:55
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.