Pop up Quiz on Triangles

Expert replies

aardvax: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Thu Dec 27, 2007 8:37 pm; GMAT Score:510

by aardvax » Sat Sep 04, 2010 2:22 am

Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle?

I. 2

II. 12

III. 24

II only

A. II only
B. I and II only
C. II and III only
D. I and III only
E. I, II and III.

Please post your answers, I feel that the third side should be >= 3 for making the figure pass the rule

Any side of a triangle will always be less than the sum of the other two sides but greater than the difference of the other two sides.

Can we make triangles of sides ?
8,6,1
8,6,2

i think the answer should be C here, however the explanation considered E (taking area as 0<Area<=24)

Source: Beat The GMAT — Problem Solving | Sat Sep 04, 2010 2:22 am

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Sat Sep 04, 2010 2:51 am

aardvax wrote:Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle?

I. 2

II. 12

III. 24

II only

A. II only
B. I and II only
C. II and III only
D. I and III only
E. I, II and III.

Please post your answers, I feel that the third side should be >= 3 for making the figure pass the rule

Any side of a triangle will always be less than the sum of the other two sides but greater than the difference of the other two sides.

Can we make triangles of sides ?
8,6,1
8,6,2

i think the answer should be C here, however the explanation considered E (taking area as 0<Area<=24)

The third side could measure x, such that x < 6 + 8 or x < 14, and x > 8 – 6 or x > 2; hence, x cannot take 2 or less.

2 is also a possible area as it’s height could be as small as ½ for 8 as base, where 8 is one of the sides of the triangle. The maximum area of a triangle with sides 6 and 8 is 24, when the sides include right angle.

[spoiler]E[/spoiler]

The mind is everything. What you think you become. –Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

aardvax: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Thu Dec 27, 2007 8:37 pm; GMAT Score:510

by aardvax » Sat Sep 04, 2010 1:27 pm

thanks sanju fr the explanation.. i was just too obsessed with making one of the sides as height while calculating the area...
in 1/2 x b x h

I am clear now.... there is no need to consider the third side while calculating the min area...

Featured schoolRound 2 closes Jan 7, 2027 53 days left

Chicago Booth

Since 1982, 10 Booth faculty members have received the Nobel Prize in Economic Sciences, more than any other business school.

#3
U.S. News rank: $175,000
Median base salary: 670
Average GMAT Focus: 635
Students in the class

Apply to Booth Visit chicagobooth.edu See the full profile

Photo: Warren LeMay, CC BY-SA 2.0

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review