Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 04 May 2015, 03:51

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Figure ABCD is a rectangle with sides of length x centimete

Author Message
TAGS:
Intern
Joined: 18 Jun 2007
Posts: 2
Followers: 0

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

Figure ABCD is a rectangle with sides of length x centimete [#permalink]  15 Jul 2007, 18:45
00:00

Difficulty:

25% (medium)

Question Stats:

69% (02:02) correct 31% (01:25) wrong based on 155 sessions
Attachment:

Untitled.png [ 7.04 KiB | Viewed 1450 times ]
Figure ABCD is a rectangle with sides of length x centimeters and width y centimeters, and a diagonal of length z centimeters. What is the measure, in centimeters, of the perimeter of ABCD ?

(1) x – y = 7
(2) z = 13
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Feb 2014, 04:28, edited 2 times in total.
Renamed the topic, edited the question, added the figure and the OA.
Intern
Affiliations: IChemE
Joined: 30 Jan 2014
Posts: 2
Location: United Arab Emirates
Concentration: Finance, Strategy
WE: Engineering (Energy and Utilities)
Followers: 0

Kudos [?]: 5 [0], given: 0

Re: Figure ABCD is a rectangle with sides of length x [#permalink]  03 Feb 2014, 03:12
dynocomet wrote:
Figure ABCD is a rectangle with sides of length x centimeters and width y centimeters, and a diagonal of length z centimeters. What is the measure, in centimeters, of the perimeter of ABCD? (The diagram shows line segment AD labeled as "x" and line segment DC labeled as "y")

(1) x - y = 7
(2) z = 13

I read that the answer is C, but cannot understand why. First of all, statement 1 seems like a contradiction -- how can the hypotenuse be SMALLER than either of the two sides?

Thanks.

The answer to the questions shows C. However why can we not state that from statement (2) we are dealing with a 5,12,13 triangle? Hence B would be sufficient to answer the question.
Math Expert
Joined: 02 Sep 2009
Posts: 27192
Followers: 4225

Kudos [?]: 40975 [0], given: 5635

Re: Figure ABCD is a rectangle with sides of length x [#permalink]  03 Feb 2014, 04:37
Expert's post
1
This post was
BOOKMARKED
Mattd wrote:
dynocomet wrote:
Figure ABCD is a rectangle with sides of length x centimeters and width y centimeters, and a diagonal of length z centimeters. What is the measure, in centimeters, of the perimeter of ABCD? (The diagram shows line segment AD labeled as "x" and line segment DC labeled as "y")

(1) x - y = 7
(2) z = 13

I read that the answer is C, but cannot understand why. First of all, statement 1 seems like a contradiction -- how can the hypotenuse be SMALLER than either of the two sides?

Thanks.

The answer to the questions shows C. However why can we not state that from statement (2) we are dealing with a 5,12,13 triangle? Hence B would be sufficient to answer the question.

The point is that a right triangle with hypotenuse 13, doesn't mean that we have (5, 12, 13) right triangle. If we are told that the lengths of all sides are integers, then yes: the only integer solution for right triangle with hypotenuse 13 would be (5, 12, 13). Or in other words: $$x^2+y^2=13^2$$ DOES NOT mean that $$x=5$$ and $$y=12$$. Certainly this is one of the possibilities but definitely not the only one. In fact $$x^2+y^2=13^2$$ has infinitely many solutions for $$x$$ and $$y$$ and only one of them is $$x=5$$ and $$y=12$$.

For example: $$x=1$$ and $$y=\sqrt{168}$$ or $$x=2$$ and $$y=\sqrt{165}$$...

So knowing that the diagonal of a rectangle (hypotenuse) equals to one of the Pythagorean triple hypotenuse values is not sufficient to calculate the sides of this rectangle.

Hope it's clear.
_________________
Intern
Affiliations: IChemE
Joined: 30 Jan 2014
Posts: 2
Location: United Arab Emirates
Concentration: Finance, Strategy
WE: Engineering (Energy and Utilities)
Followers: 0

Kudos [?]: 5 [0], given: 0

Re: Figure ABCD is a rectangle with sides of length x centimete [#permalink]  03 Feb 2014, 04:52
Thanks for the help. Did not think about the integer part.
Senior Manager
Joined: 25 Sep 2012
Posts: 277
Location: India
Concentration: Strategy, Marketing
Schools: Ivey '18
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
Followers: 0

Kudos [?]: 82 [0], given: 237

Re: Figure ABCD is a rectangle with sides of length x centimete [#permalink]  15 Jul 2014, 01:13
How can we use the both statement to find the answer?
I marked B and Bunuel explained how it is wrong. My second answer would be E
I mean I know 12-5 = 7 and that with z =13 so we can say that three sides "can" be 5,12,13 but can we say that's the only possible value?
Math Expert
Joined: 02 Sep 2009
Posts: 27192
Followers: 4225

Kudos [?]: 40975 [0], given: 5635

Figure ABCD is a rectangle with sides of length x centimete [#permalink]  15 Jul 2014, 01:35
Expert's post
b2bt wrote:
How can we use the both statement to find the answer?
I marked B and Bunuel explained how it is wrong. My second answer would be E
I mean I know 12-5 = 7 and that with z =13 so we can say that three sides "can" be 5,12,13 but can we say that's the only possible value?

Given that $$x - y = 7$$ and $$z = 13$$. We also know that $$x^2 + y^2 = z^2 = 169$$. We want to find the perimeter which is $$2x+2y = 2(x+y)$$.

Square $$x - y = 7$$ --> $$x^2 - 2xy + y^2 = 49$$ --> $$169 - 2xy = 49$$ --> $$2xy = 120$$.

Add $$2xy = 120$$ to$$x^2 + y^2 = 169$$: $$x^2 + 2xy + y^2 = 169 + 120$$ --> $$(x+y)^2 = 289$$ --> $$x+y = 17$$ --> $$2(x+y) = 24$$.

Hope it's clear.
_________________
Intern
Joined: 25 May 2014
Posts: 3
Followers: 0

Kudos [?]: 0 [0], given: 20

Re: Figure ABCD is a rectangle with sides of length x centimete [#permalink]  22 Jul 2014, 08:31
I looked at z=13 as
x^2+y^2=z^2=169
(x+y)(x-y)=169
(x+y)=169/7..... as from 1. we know that x-y=7

hence perimeter is 2(x+y)= 2(169/7)....

Hence C
Re: Figure ABCD is a rectangle with sides of length x centimete   [#permalink] 22 Jul 2014, 08:31
Similar topics Replies Last post
Similar
Topics:
8 Figure ABCD is a square with sides of length x. Arcs AB, AD, 1 02 Aug 2014, 07:30
9 In the figure, each side of square ABCD has length 1, the length of li 8 25 Jan 2010, 09:05
1 ABCD forms a rectangle with sides x and y. z is the 5 15 Feb 2008, 03:55
In the figure, each side of square ABCD has length 1, the 2 27 Nov 2007, 13:42
55 In the figure, each side of square ABCD has length 1, the length of li 17 19 Oct 2007, 03:37
Display posts from previous: Sort by