It is currently 19 Nov 2017, 05:53

### 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 diagonal m

Author Message
TAGS:

### Hide Tags

Manager
Joined: 26 Mar 2008
Posts: 99

Kudos [?]: 258 [1], given: 0

Schools: Tuck, Duke
A small, rectangular park has a perimeter of 560 feet and a diagonal m [#permalink]

### Show Tags

27 Sep 2008, 13:05
1
KUDOS
6
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

75% (01:41) correct 25% (02:47) wrong based on 110 sessions

### HideShow timer Statistics

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-small-rectangular-park-has-a-perimeter-of-560-feet-and-a-91118.html
[Reveal] Spoiler: OA

Kudos [?]: 258 [1], given: 0

VP
Joined: 05 Jul 2008
Posts: 1402

Kudos [?]: 443 [2], given: 1

Re: A small, rectangular park has a perimeter of 560 feet and a diagonal m [#permalink]

### Show Tags

27 Sep 2008, 13:45
2
KUDOS
1
This post was
BOOKMARKED
arorag 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. 19,200
B. 19,600
C. 20,000
D. 20,400
E. 20,800

2 (l+w) = 560 means l+w = 280

Sqrt ( l^2 + w^2) = 200 means (l2^+w^2) = 40000

square both sides of (l+w) =280

l^2 + w^2 +2lw = 78400

means 2lw= 38400 lw=19,200

Hence A

Kudos [?]: 443 [2], given: 1

Senior Manager
Joined: 09 Oct 2007
Posts: 463

Kudos [?]: 56 [1], given: 1

Re: A small, rectangular park has a perimeter of 560 feet and a diagonal m [#permalink]

### Show Tags

27 Sep 2008, 13:45
1
KUDOS
A:

I thought the 200 as the hypotenuse was a little 'fishy', so I started thinking of it as a 3-4-5 triangle: 200 as the hypotenuse, 120 and 160 as the legs and it worked: 120*160 = 19,200.

Kudos [?]: 56 [1], given: 1

Manager
Joined: 27 Sep 2008
Posts: 76

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

Re: A small, rectangular park has a perimeter of 560 feet and a diagonal m [#permalink]

### Show Tags

27 Sep 2008, 14:08
same here:

a+b = 280

(a+b)(a+b) =78'400

a^2+2ab+b^2 = 78'400

a^2+b^2 = 200^2 = 40'000

2ab = 38'400

ab = 19'200

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

Non-Human User
Joined: 09 Sep 2013
Posts: 15689

Kudos [?]: 282 [0], given: 0

Re: A small, rectangular park has a perimeter of 560 feet and a diagonal m [#permalink]

### Show Tags

13 Nov 2014, 13:03
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.
_________________

Kudos [?]: 282 [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 42247

Kudos [?]: 132662 [4], given: 12331

Re: A small, rectangular park has a perimeter of 560 feet and a diagonal m [#permalink]

### Show Tags

13 Nov 2014, 13:09
4
KUDOS
Expert's post
5
This post was
BOOKMARKED
arorag 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. 19,200
B. 19,600
C. 20,000
D. 20,400
E. 20,800

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: $$(x^2+2xy+y^2)-(x^2+y^2)=280^2-200^2$$ --> $$2xy=(280-200)(280+200)$$ --> $$2xy=80*480$$ --> $$xy=40*480=19200$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-small-rectangular-park-has-a-perimeter-of-560-feet-and-a-91118.html
_________________

Kudos [?]: 132662 [4], given: 12331

Re: A small, rectangular park has a perimeter of 560 feet and a diagonal m   [#permalink] 13 Nov 2014, 13:09
Display posts from previous: Sort by