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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

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).

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???

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...!!!
_________________

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

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.
_________________

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)?

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

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

Show Tags

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.

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

Show Tags

15 Dec 2015, 07:59

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.
_________________

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

Show Tags

02 Feb 2016, 17:56

Bunuel wrote:

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

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).

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

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).

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

Show Tags

03 Feb 2016, 19:50

1

This post received KUDOS

1

This post was BOOKMARKED

you can avoid a lot of work in this problem by recognizing that, with the info provided, the diagonal forms a triangle inside the rectangle with sides that have a 3:4:5 ratio.

diagonal = 200 2x + 2y = 560, or x + y = 280 a^2 + b^2 = c^2 for each the sides of the triangle

using the ratio 3:4:5 for sides, and knowing c = 200, you can deduce the following

a=120 b=160

160x120=19,200

A is the answer.

gmatclubot

Re: A small, rectangular park has a perimeter of 560 feet and a
[#permalink]
03 Feb 2016, 19:50

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Happy 2017! Here is another update, 7 months later. With this pace I might add only one more post before the end of the GSB! However, I promised that...