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

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A small, rectangular park has a perimeter of 560 feet and a [#permalink] New post 06 Mar 2010, 04:21
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69% (03:07) correct 31% (01:35) wrong based on 75 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.
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Re: Rectangular park [#permalink] New post 06 Mar 2010, 04:45
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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 ?

Thanks in advance

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.

Answer: A.

Hope it helps.
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Re: Rectangular park [#permalink] New post 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??? :-(
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Re: Rectangular park [#permalink] New post 14 May 2010, 08:44
great explanation thanks
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Re: Rectangular park [#permalink] New post 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...!!!
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Re: Rectangular park [#permalink] New post 26 Dec 2010, 00:10
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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
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Re: Rectangular park [#permalink] New post 13 Nov 2013, 15:47
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Re: Rectangular park [#permalink] New post 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)?
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Re: Rectangular park [#permalink] New post 26 Mar 2014, 08:05
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 :P
Re: Rectangular park   [#permalink] 26 Mar 2014, 08:05
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