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:

Given line L, and a parallel line that runs through point [#permalink]

Show Tags

13 Apr 2013, 05:16

3

This post received KUDOS

7

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

85% (hard)

Question Stats:

56% (03:49) correct
44% (02:09) wrong based on 109 sessions

HideShow timer Statistics

Attachment:

CG.png [ 47.72 KiB | Viewed 2380 times ]

Given line L (illustrated in graph), and a parallel line that runs through point (-1,5), what is the perimeter of a rectangle whose sides run along the two lines and has a length of 9?

Re: Given line L, and a parallel line that runs through point [#permalink]

Show Tags

15 Apr 2013, 07:19

4

This post received KUDOS

Expert's post

12bhang wrote:

Attachment:

CG.png

Given line L (illustrated in graph), and a parallel line that runs through point (-1,5), what is the perimeter of a rectangle whose sides run along the two lines and has a length of 9?

A. 28 B. 9*(15)^0.5 C. 18+2*(20)^0.5 D. 36 E. 45

The question asks nothing more than calculating the perpendicular distance between the point (-1,5) and the line 3x-4y-2=0. This distance = \(|3(-1)-4(5)-2|/\sqrt{3^2+4^2}\)= |-25|/5 = 5. Thus the perimeter is 2*(5+9) = 28. A. _________________

Re: Given line L, and a parallel line that runs through point [#permalink]

Show Tags

13 Apr 2013, 05:57

2

This post received KUDOS

The parallel line is found using the formula y-y0=m(x-x0) , y-5=3/4(x+1) The question comes down to what is the distance between \(y=\frac{3}{4}x-\frac{1}{2}\) and \(y=\frac{3}{4}x+\frac{23}{4}\)? I was not able to find a quick and easy solution to this question, so I took the perpendicular line \(y=-4/3x\) and calculated the intersections. 3/4x+23/4=-4/3x point\((-\frac{69}{25},\frac{92}{25})\) 3/4x-1/2=-4/3x pont\((\frac{6}{25},-\frac{8}{25})\) Now using Pitagora we must find the hypotenuse of this triangle which has lengths \(\frac{92+8}{25}=4\) and \(\frac{69+6}{25}=3\) (refer to the picture and sorry for the bad quality...) So hypotenuse = 5 and perimeter = 9+9+5+5=28

Attachments

CG.png [ 58.88 KiB | Viewed 2337 times ]

_________________

It is beyond a doubt that all our knowledge that begins with experience.

Re: Given line L, and a parallel line that runs through point [#permalink]

Show Tags

15 Apr 2013, 13:12

12bhang wrote:

Attachment:

CG.png

Given line L (illustrated in graph), and a parallel line that runs through point (-1,5), what is the perimeter of a rectangle whose sides run along the two lines and has a length of 9?

A. 28 B. 9*(15)^0.5 C. 18+2*(20)^0.5 D. 36 E. 45

Another way to work out.... The equation of line parallel to y=3/4x-1/2 passing through -1,5 will be y=3/4x+23/4 Now distance between two parallel lines y=mx+c and y=mx+c1 is given by = |c1-c| / sq rt(m^2+1)

here we have |23/4 + 1/2| /sq root (3/4^2 + 1) which comes out to be 5. Perimeter is 9*2 + 5*2 = 28 _________________

Re: Given line L, and a parallel line that runs through point [#permalink]

Show Tags

27 Apr 2013, 23:01

12bhang wrote:

Attachment:

CG.png

Given line L (illustrated in graph), and a parallel line that runs through point (-1,5), what is the perimeter of a rectangle whose sides run along the two lines and has a length of 9?

A. 28 B. 9*(15)^0.5 C. 18+2*(20)^0.5 D. 36 E. 45

The slope will be same for parallel lines. Hence, we can write the equation of the line which passes through point (-1.5) as y = 3/4x+b. After substituting the values of x&y, the equation will become, 5=3/4*-1 + b 5 = -3/4 + b b = 23/4

The question already provides the length of one side and which is equal to 9. Now, we have to find the length of the other side.

In other words, it requires us to find the distance b/w two parallel lines, y = 3/4x - 1/2 & y = 3/4x + 23/4.

The formula to find the distance b/w two parallel lines is |b-c| / √(m²+1)

|23/4 + 1/2| / √(3/4)²+1) = (25/4) / √(25/16) = 5

Hence, the perimeter of the rectangle in the xy plane will become = 2 (9 + 5) = 2*14 = 28

Re: Given line L, and a parallel line that runs through point [#permalink]

Show Tags

14 Apr 2014, 06:17

Here's the way I solved this one.

We basically have a rectangle and we need to find the perimeter 2 (L+W). We know the length is 9, so we need to find the width which is equal to the distance between the two parallel lines

Thus we know that the other line running through (-1,5) is y=3/4x+b

Distance between two parallel lines is 25/4 / sqrt (9/16+1) = 5

Re: Given line L, and a parallel line that runs through point [#permalink]

Show Tags

14 Apr 2014, 23:48

Slope of perpendicular line to 3/4x-1/2 is equal to -4/3 and this means that we have two legs 4 and 3 and hypotenuse 5 which is side of rectangle, so perimeter is 2*9+2*5=28. Answer is A

Problem is that slope -4/3 can result in hypotenuse equal to 5,10, 15, 20 etc. But only option that fits to answer choices is 5

Re: Given line L, and a parallel line that runs through point [#permalink]

Show Tags

12 Jun 2015, 00:29

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: Given line L, and a parallel line that runs through point [#permalink]

Show Tags

13 Jun 2015, 06:02

1 - We need to calculate the second equation line. Since it is parallel to the other one, slope is 3/4[x] and C is Y = 3/4[X] + C i.e. 5 = 3/4[-1] + C C = 23/4 Y = 3/4[X] + 23/4

2 - Then calculate the distance between two parallel lines |b-c|/ [M²+1]sqrt(2) |-1/2 - 23/4| / [3/4 + 1]sqrt(2) = 5 5 is the perpendicular distance between the two lines

3 - Calculate the perimeter 2x[5+9] = 28

gmatclubot

Re: Given line L, and a parallel line that runs through point
[#permalink]
13 Jun 2015, 06:02

Last year when I attended a session of Chicago’s Booth Live , I felt pretty out of place. I was surrounded by professionals from all over the world from major...

I recently returned from attending the London Business School Admits Weekend held last week. Let me just say upfront - for those who are planning to apply for the...