• 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

Patricia builds two triangles, each with 30 feet of wood.

This topic has 2 expert replies and 0 member replies

Patricia builds two triangles, each with 30 feet of wood.

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



Patricia builds two triangles, each with 30 feet of wood. The first triangle ABC is built to maximize the length of the base side. The second triangle DEF is built to maximize the area of the triangle. What is the ratio of the length of the base of triangle ABC to the length of the base of triangle DEF? The lengths of all line segments are integers.

A. 1:1
B. 6:5
C. 5:4
D. 7:5
E. 2:1

The OA is D

Source: Veritas Prep

  • +1 Upvote Post
  • Quote
  • Flag
Post
swerve wrote:
Patricia builds two triangles, each with 30 feet of wood. The first triangle ABC is built to maximize the length of the base side. The second triangle DEF is built to maximize the area of the triangle. What is the ratio of the length of the base of triangle ABC to the length of the base of triangle DEF? The lengths of all line segments are integers.

A. 1:1
B. 6:5
C. 5:4
D. 7:5
E. 2:1

The OA is D

Source: Veritas Prep
So, we have two triangles with the perimeter 30 feet given that the sides of the triangles are integers.

1. Triangle-1 has the maximum possible base:

The maximum possible base would be a little less than half the perimeter of the triangle.

Thus, the maximum possible base < 1/2 of 30 (= 15)

The maximum possible base or base of ∆ABC = 14 since it is given that the sides of the triangles are integers.

1. Triangle-2 has the maximum possible area:

For the given perimeter 30, the maximum possible area would be for a triangle that has the same sides; thus, it is an equilateral triangle.

Thus, side of an equilateral triangle of ∆DFF = 30/3 = 10 feet

Ratio of the length of the base of triangle ABC to the length of the base of triangle DEF = 14/10 = 7 : 5.

The correct answer: D

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: GMAT Manhattan | [url=https://www.manhattanreview.com/chicago-gre-prep-courses/ ]GRE Prep Courses Chicago[/url] | ACT Prep Courses Seattle | Boston IELTS Tutoring | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

  • +1 Upvote Post
  • Quote
  • Flag
Post
swerve wrote:
Patricia builds two triangles, each with 30 feet of wood. The first triangle ABC is built to maximize the length of the base side. The second triangle DEF is built to maximize the area of the triangle. What is the ratio of the length of the base of triangle ABC to the length of the base of triangle DEF? The lengths of all line segments are integers.

A. 1:1
B. 6:5
C. 5:4
D. 7:5
E. 2:1

The OA is D

Source: Veritas Prep
Since triangle ABC maximizes the length of the base, and a side of the triangle must be less than the sum of the other two sides, then the maximum length of the base will be 14, which is 1 less than half of the perimeter.

The triangle with a fixed perimeter that maximizes the area is an equilateral triangle since, if a polygon is given a fixed perimeter, the polygon with the largest area must be regular (note: a “regular” triangle is an equilateral triangle). So a side (or base) of triangle DEF = 10.

Therefore, the ratio of the the two bases = 14/10 = 7/5.

Answer: D

_________________

Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com



See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

  • +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
  • 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
  • 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
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

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

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT

Top First Responders*

1 Jay@ManhattanReview 68 first replies
2 Brent@GMATPrepNow 65 first replies
3 GMATGuruNY 41 first replies
4 Ian Stewart 23 first replies
5 Scott@TargetTestPrep 15 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

200 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

91 posts
3 image description Max@Math Revolution

Math Revolution

85 posts
4 image description Jay@ManhattanReview

Manhattan Review

73 posts
5 image description GMATGuruNY

The Princeton Review Teacher

65 posts
See More Top Beat The GMAT Experts