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

 It is currently 01 Aug 2015, 04:54

### 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

# A small, rectangular park has a perimeter of 560 feet and a

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Intern
Joined: 08 Dec 2009
Posts: 29
Followers: 0

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

A small, rectangular park has a perimeter of 560 feet and a [#permalink]  06 Mar 2010, 04:21
1
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

69% (03:05) correct 31% (02:09) wrong based on 159 sessions
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. 19,200
B. 19,600
C. 20,000
D. 20,400
E. 20,800
[Reveal] Spoiler: OA

Last edited by Bunuel on 14 Nov 2013, 00:59, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Math Expert
Joined: 02 Sep 2009
Posts: 28781
Followers: 4594

Kudos [?]: 47427 [10] , given: 7123

Re: Rectangular park [#permalink]  06 Mar 2010, 04:45
10
KUDOS
Expert's post
6
This post was
BOOKMARKED
aljatar wrote:
Hi everyone, I am struggling with this one, found the answer but I am looking for a fast way to do it ?

Can anyone help ?

R.

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. 19,200
B. 19,600
C. 20,000
D. 20,400
E. 20,800

[Reveal] Spoiler:
OA is A

Hi, and welcome to Gmat Club.

The question you posted can be solved as follows:
Given:
(1) $$2x+2y=560$$ (perimeter) --> $$x+y=280$$
(2) $$x^2+y^2=200^2$$ (diagonal, as per Pythagoras).

Question: $$xy=?$$

Square (1) --> $$x^2+2xy+y^2=280^2$$. Now subtract (2) fro this: $$(x^2+2xy+y^2)-(x^2+y^2)=280^2-200^2$$ --> $$2xy=(280-200)(280+200)$$ --> $$2xy=80*480$$ --> $$xy=40*480=19200$$.

Hope it helps.
_________________
Manager
Joined: 14 Apr 2010
Posts: 230
Followers: 2

Kudos [?]: 64 [0], given: 1

Re: Rectangular park [#permalink]  14 May 2010, 02:04
I have a small confusion. The diagonal is given and it divides the rectangle into two 30-60-90 triangles. Can't we find the measure of two other sides? What am i missing here???
Manager
Joined: 16 Feb 2010
Posts: 173
Followers: 2

Kudos [?]: 25 [0], given: 10

Re: Rectangular park [#permalink]  14 May 2010, 08:44
great explanation thanks
Intern
Affiliations: Scrum Alliance
Joined: 09 Feb 2010
Posts: 33
Location: United States (MI)
Concentration: Strategy, Technology
WE: Information Technology (Retail)
Followers: 1

Kudos [?]: 12 [0], given: 14

Re: Rectangular park [#permalink]  14 May 2010, 09:14
bibha wrote:
I have a small confusion. The diagonal is given and it divides the rectangle into two 30-60-90 triangles. Can't we find the measure of two other sides? What am i missing here???
Does the diagonal of a rectangle always divide it into two 30-90-60 triangles ? Think again...!!!
Manager
Joined: 23 Oct 2010
Posts: 87
Location: India
Followers: 3

Kudos [?]: 23 [4] , given: 6

Re: Rectangular park [#permalink]  26 Dec 2010, 00:10
4
KUDOS
The fastest way:

we know 560 is an integer (no fraction) and hence probability of sides of rectangle being integer is quite high
200 is diagonal - recognizing it from pythagorean patterns it seems to be a multiple of 10 (10 - 8 - 6)
= 10 * 2 * 10
hence other sides of the pythagorean triplet will be:
8 * 2 * 10
and
6 * 2 * 10
= 160
= 120
bingo - (160 + 120 ) * 2 = 560
hence area = 160 * 120 = 19200
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 5705
Followers: 322

Kudos [?]: 62 [0], given: 0

Re: Rectangular park [#permalink]  13 Nov 2013, 15:47
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.
_________________
SVP
Joined: 06 Sep 2013
Posts: 2046
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 30

Kudos [?]: 323 [0], given: 355

Re: Rectangular park [#permalink]  21 Nov 2013, 13:06
sleekmover wrote:
The fastest way:

we know 560 is an integer (no fraction) and hence probability of sides of rectangle being integer is quite high
200 is diagonal - recognizing it from pythagorean patterns it seems to be a multiple of 10 (10 - 8 - 6)
= 10 * 2 * 10
hence other sides of the pythagorean triplet will be:
8 * 2 * 10
and
6 * 2 * 10
= 160
= 120
bingo - (160 + 120 ) * 2 = 560
hence area = 160 * 120 = 19200

Yeah there has to be a shorter way to solve this one but where did you get the 10*2*10 stuff for each side on the (10 - 8 - 6)?
SVP
Joined: 06 Sep 2013
Posts: 2046
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 30

Kudos [?]: 323 [1] , given: 355

Re: Rectangular park [#permalink]  26 Mar 2014, 08:05
1
KUDOS
hideyoshi wrote:
bibha wrote:
I have a small confusion. The diagonal is given and it divides the rectangle into two 30-60-90 triangles. Can't we find the measure of two other sides? What am i missing here???
Does the diagonal of a rectangle always divide it into two 30-90-60 triangles ? Think again...!!!

No I don't think so buddy, there's nothing clear when it is a rectangle. If its a square I'm pretty sure that the two right triangles that are divided by the diagonal are in fact two 45-45-90 triangles, but with the rectangle I don't think one can be sure about the angle

Hope this helps
Cheers
J
Intern
Joined: 02 Oct 2014
Posts: 4
Followers: 0

Kudos [?]: 2 [0], given: 1

Re: A small, rectangular park has a perimeter of 560 feet and a [#permalink]  11 Dec 2014, 03:47
1
This post was
BOOKMARKED
It is a really good exercise.

Solving this one in a standard way brings a lot of confusion.
In my opinion it is a helpful here to know, that a square has a biggest area if the sum of length of bases is the same.
For example: If sum of bases is 8, the biggest possible area is 16, which is a square. (Other options 5x3=15; 6x2=12; 8x1=8)

Knowing this, we could easily eliminate answer choices that are other 200 because we know that diagonal is 200 and therefore the maximum area is 200^2/2
Moreover, knowing the rule of square diagonal we could remove 200, because square diagonal would be base * sqrt(2) (90-45-45 formula)

And also 196 is a (14*14) so this means that diagonal is not integer and we could remove it also.

Hence, one answer choice is left:)

A :D
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1859
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 23

Kudos [?]: 1012 [0], given: 193

Re: A small, rectangular park has a perimeter of 560 feet and a [#permalink]  11 Dec 2014, 18:53
Say length of the park = x, width = (280-x)

$$200^2 = x^2 + (280-x)^2$$

$$2x^2 - 560x + (280^2 - 200^2) = 0$$

$$2x^2 - 560x + (280 + 200)(280 - 200) = 0$$

$$2x^2 - 560x + 480 * 80 = 0$$

$$x^2 - 280x + 480*40 = 0$$

Dimensions = 160 & 120

Area = 19200

_________________

Kindly press "+1 Kudos" to appreciate

Re: A small, rectangular park has a perimeter of 560 feet and a   [#permalink] 11 Dec 2014, 18:53
Similar topics Replies Last post
Similar
Topics:
5 If the perimeter of a rectangular garden plot is 34 feet and 7 05 Jan 2014, 12:10
6 A rectangular box has dimensions of 8 feet, 8 feet, and z 3 02 Mar 2012, 14:53
9 The area of a square garden is A square feet and the perimet 16 28 Apr 2010, 07:39
9 A small, rectangular park has a perimeter of 560 feet and a diagonal m 5 27 Sep 2008, 12:05
2 The area of a square garden is A square feet and the perimet 6 19 Apr 2006, 20:50
Display posts from previous: Sort by

# A small, rectangular park has a perimeter of 560 feet and a

 Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO 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®.