• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

A triangle of area 30 is formed by the line x/c + y/(c+7) -

This topic has 2 expert replies and 0 member replies

GMAT/MBA Expert

A triangle of area 30 is formed by the line x/c + y/(c+7) -

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



GMATH practice exercise (Quant Class 20)

A triangle of area 30 is formed by the line x/c + y/(c+7) - 1 = 0 (where c is a positive constant) and the coordinate axes. What is the perimeter of this triangle?

(A) 12
(B) 24
(C) 30
(D) 36
(E) 52

Answer: _____(C)__

_________________
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
fskilnik@GMATH wrote:
[size=17]GMATH practice exercise (Quant Class 20)

A triangle of area 30 is formed by the line x/c + y/(c+7) - 1 = 0 (where c is a positive constant) and the coordinate axes. What is the perimeter of this triangle?

(A) 12
(B) 24
(C) 30
(D) 36
(E) 52
Given that the area and the answer choices are all integers, the triangle is probably a Pythagorean Triple.
The only Pythagorean Triple with an area of 30 is 5-12-13.

In the given equation, test c=5, with the result that c+7 = 12:
x/5 + y/12 - 1 = 0

If x=0, then y=12, implying a y-intercept at (0, 12).
If y=0, then x=5, implying an x-intercept at (5, 0).
Implication:
In combination with the two axes, the line above will form a right triangle that has a height of 12 along the y-axis, a base of 5 along the x-axis, and a hypotenuse of 13, with the result that the area = (1/2)(12)(5) = 30.
Perimeter = 5+12+13 = 30.

The correct answer is C.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

GMAT/MBA Expert

GMAT Instructor
Joined
09 Oct 2010
Posted:
1449 messages
Followed by:
32 members
Upvotes:
59
Post
fskilnik@GMATH wrote:
GMATH practice exercise (Quant Class 20)

A triangle of area 30 is formed by the line x/c + y/(c+7) - 1 = 0 (where c is a positive constant) and the coordinate axes. What is the perimeter of this triangle?

(A) 12
(B) 24
(C) 30
(D) 36
(E) 52
Yes... 5-12-13 is an important GMAT Pythagorean Triple...

$$?\,\, = \,\,\Delta \,\,{\rm{perimeter}}$$
$${S_\Delta } = 30\,\,\,\left( * \right)$$

$${x \over c} + {y \over {c + 7}} = 1\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{
\,x{\rm{ - intercept}} = c \hfill \cr
\,y{\rm{ - intercept}} = c + 7 \hfill \cr} \right.\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,30 = {{c\left( {c + 7} \right)} \over 2}\,\,\,$$
$$c\left( {c + 7} \right) = 60\,\,\,\left[ { = 5 \cdot 12 = \left( { - 12} \right)\left( { - 5} \right)} \right]\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,c = 5\,\,\,{\rm{or}}\,\,\,c = - 12\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{stem}}} \,\,\,\,\,c = 5$$

$$\left\{ \matrix{
\,{\rm{right}}\,\,\Delta \hfill \cr
\,{\rm{legs}}\,\,5,12 \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{hyp}}\,\, = 13\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,? = 5 + 12 + 13 = 30$$


The correct answer is (C).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

_________________
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

  • +1 Upvote Post
  • Quote
  • Flag
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors

Top First Responders*

1 Brent@GMATPrepNow 43 first replies
2 Ian Stewart 35 first replies
3 Jay@ManhattanReview 32 first replies
4 GMATGuruNY 27 first replies
5 Scott@TargetTestPrep 13 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

189 posts
2 image description Max@Math Revolution

Math Revolution

90 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

75 posts
4 image description GMATGuruNY

The Princeton Review Teacher

44 posts
5 image description Ian Stewart

GMATiX Teacher

42 posts
See More Top Beat The GMAT Experts