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Re: Rectangular park [#permalink]
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

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???

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...!!!

Re: Rectangular park [#permalink]
26 Dec 2010, 00:10

4

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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

Re: Rectangular park [#permalink]
13 Nov 2013, 15:47

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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)?

Re: Rectangular park [#permalink]
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

gmatclubot

Re: Rectangular park
[#permalink]
26 Mar 2014, 08:05

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