NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 16:06 It is currently 26 Apr 2024, 16:06
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Triangle ABC has a perimeter of 18. Which of the following cannot be

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619238 [12]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Triangle ABC has a perimeter of 18. Which of the following cannot be [#permalink] New post   20 Jul 2017, 21:38
12
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

85% (hard)

Question Stats:

45% (01:51) correct 55% (01:44) wrong based on 201 sessions
Hide Show timer Statistics
Triangle ABC has a perimeter of 18. Which of the following cannot be the area of triangle ABC?

(A) 119/359
(B) 359/119
(C) π
(D) 12
(E) 16
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
P
pikolo2510
Senior Manager
Senior Manager
Joined: 05 Jul 2017
Posts: 457
Own Kudos [?]: 724 [5]
Given Kudos: 294
Location: India
GMAT 1: 700 Q49 V36
GPA: 4
Send PM
Re: Triangle ABC has a perimeter of 18. Which of the following cannot be [#permalink] New post   28 Jul 2017, 08:19
5
Bookmarks
2 rules to remember always in such questions
- For a given perimeter, equilateral triangle has the largest area
- For a given area, equilateral triangle has the smallest perimeter

With the above context, if perimeter is 18 then each side of an equilateral triangle will be 6

Area will be (sqrt)3*3*3/4=9(sqrt)3~15.3

Hence only option above 15 is E. Answer is E
General Discussion
User avatar
P
jedit
Manager
Manager
Joined: 14 Oct 2015
Posts: 209
Own Kudos [?]: 345 [0]
Given Kudos: 854
Schools: Stanford '20 HBS '20 Sloan '20
GPA: 3.57
Send PM
Reviews Badge
Triangle ABC has a perimeter of 18. Which of the following cannot be [#permalink] New post   21 Jul 2017, 00:49
Bunuel wrote:
Triangle ABC has a perimeter of 18. Which of the following cannot be the area of triangle ABC?

(A) 119/359
(B) 359/119
(C) π
(D) 12
(E) 16


It should be E. Even if the triangle is equilateral (side 6) in which case its area would be maximum, area cannot be 16.

\(A*\sqrt{3}/4\)

\(6*\sqrt{3}/4\) \(= 15.59\)

Rest of the values are possible by playing with large and small values of base and height.
User avatar
S
TheGuyDangerous
Current Student
Joined: 10 Sep 2019
Posts: 137
Own Kudos [?]: 33 [1]
Given Kudos: 59
Location: India
Concentration: Social Entrepreneurship, Healthcare
Schools: Fuqua '24 (D) ISB '23 (A) Darden '24 (D) Johnson '24 (D) Kenan-Flagler '24 (I) McDonough '24 (S) Tepper '24 (S)
GMAT 1: 680 Q49 V33
GMAT 2: 720 Q50 V37
GRE 1: Q167 V159
GPA: 2.59
WE:Project Management (Non-Profit and Government)
Send PM
Reviews Badge
Triangle ABC has a perimeter of 18. Which of the following cannot be [#permalink] New post   Updated on: 22 Nov 2019, 03:12
1
Bookmarks
Like pikolo2510 mentioned already, for a given perimeter, an equilateral triangle has the largest area.

=> Area = 1/2*6*3(1.7) ~= 15.3

=> The area cannot be greater than 15.3. => 16 is not a possible area!

Ans E

Originally posted by TheGuyDangerous on 22 Nov 2019, 02:55.
Last edited by TheGuyDangerous on 22 Nov 2019, 03:12, edited 1 time in total.
User avatar
G
vanam52923
Manager
Manager
Joined: 17 Jul 2017
Posts: 205
Own Kudos [?]: 93 [0]
Given Kudos: 228
Send PM
Re: Triangle ABC has a perimeter of 18. Which of the following cannot be [#permalink] New post   22 Nov 2019, 03:10
pikolo2510 wrote:
2 rules to remember always in such questions
- For a given perimeter, equilateral triangle has the largest area
- For a given area, equilateral triangle has the smallest perimeter

With the above context, if perimeter is 18 then each side of an equilateral triangle will be 6

Area will be (sqrt)3*3*3/4=9(sqrt)3~15.3

Hence only option above 15 is E. Answer is E


Bunuel

doesnot the rule say :
for given perimeter, isosceles right angled traingle has maximum area?
which one is correct ?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619238 [2]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Re: Triangle ABC has a perimeter of 18. Which of the following cannot be [#permalink] New post   22 Nov 2019, 03:14
1
Kudos
1
Bookmarks
Expert Reply
vanam52923 wrote:
pikolo2510 wrote:
2 rules to remember always in such questions
- For a given perimeter, equilateral triangle has the largest area
- For a given area, equilateral triangle has the smallest perimeter

With the above context, if perimeter is 18 then each side of an equilateral triangle will be 6

Area will be (sqrt)3*3*3/4=9(sqrt)3~15.3

Hence only option above 15 is E. Answer is E


Bunuel

doesnot the rule say :
for given perimeter, isosceles right angled traingle has maximum area?
which one is correct ?


• For a given perimeter equilateral triangle has the largest area.
• For a given area equilateral triangle has the smallest perimeter.
User avatar
G
Nirmesh83
Manager
Manager
Joined: 17 Apr 2019
Posts: 89
Own Kudos [?]: 57 [0]
Given Kudos: 16
Location: India
GMAT 1: 580 Q48 V22
Send PM
Re: Triangle ABC has a perimeter of 18. Which of the following cannot be [#permalink] New post   24 Sep 2021, 07:27
S = a+b+c/2
= 18/2
=9
Area = sqrt (s)(s-a) (s-b) (s-c)
= Sqrt 9*k
= 3 sqrtk
Means area is factor of 3
So ,16 can' t be the area
So Answer is E
Bunuel : please correct me.

Posted from my mobile device
User avatar
L
Fdambro294
VP
VP
Joined: 10 Jul 2019
Posts: 1392
Own Kudos [?]: 542 [0]
Given Kudos: 1656
Send PM
Re: Triangle ABC has a perimeter of 18. Which of the following cannot be [#permalink] New post   10 Oct 2021, 18:50
Given a constant addition of terms ———-> any product of those terms will be maximized if we make those terms equal to themselves


In this case, let the side lengths of the triangle be: A , B, C

A + B + C = 18


Given this constant addition of the three variables that sum to the triangle’s perimeter, we will maximize the product of the unknown quantities of we make them equal.

Let A = B = C = 6

The area of an equilateral triangle with side 6 is the MAX Area that this triangle can have

MAX area = (6)^2 * sqrt(3) * (1/4)

MAX area = 9 * sqrt(3) ~ 15.3 (an overestimate)

0 < Area of triangle < 15.3

This, the answer is E

Triangle can not take an area of 16

Posted from my mobile device
avatar
B
Rokacky
Intern
Intern
Joined: 10 Nov 2018
Posts: 15
Own Kudos [?]: 2 [0]
Given Kudos: 0
Send PM
Re: Triangle ABC has a perimeter of 18. Which of the following cannot be [#permalink] New post   11 Oct 2021, 00:10
The triangle will have the maximum area if it is a equilateral triangle.
Hence Option E.
GMAT Club Bot
gmatclubot
Re: Triangle ABC has a perimeter of 18. Which of the following cannot be [#permalink]
11 Oct 2021, 00:10
Moderators:
Bunuel
Math Expert
92948 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions