NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 16:59 It is currently 25 Apr 2024, 16:59
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

What is the maximum right triangles with legs of length 3 ft

User avatar
duttsit
Senior Manager
Senior Manager
Joined: 22 Aug 2005
Posts: 496
Own Kudos [?]: 660 [0]
Given Kudos: 0
Location: CA
Send PM
What is the maximum right triangles with legs of length 3 ft [#permalink] New post   05 Nov 2005, 21:32
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 2 sessions
Hide Show timer Statistics
What is the maximum right triangles with legs of length 3 ft and 4 ft that can be cut from the rectangular sheet of metal of dimension 7 ft x 12 ft.

(A) 7
(B) 8
(C) 10
(D) 12
(E) 14

time: 3 mins for ans with reasons :)



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
tank
Intern
Intern
Joined: 01 Jun 2005
Posts: 17
Own Kudos [?]: 2 [0]
Given Kudos: 0
Send PM
Re: What is the maximum right triangles with legs of length 3 ft [#permalink] New post   Updated on: 05 Nov 2005, 22:31
duttsit wrote:
What is the maximum right triangles with legs of length 3 ft and 4 ft that can be cut from the rectangular sheet of metal of dimension 7 ft x 12 ft.

(A) 7
(B) 8
(C) 10
(D) 12
(E) 14

time: 3 mins for ans with reasons :)


Ans is E.

Area of triangle = 1/2 x 3x 4 = 6[Note, since it is a right triangle the lengths are in the ratio 3:4:5. Therefore, 3 or 4 could not be the hypotenuse]

Area of the rect = 12x7 = 84

# of triangles from that sheet = 84/6 = 14

Originally posted by tank on 05 Nov 2005, 22:01.
Last edited by tank on 05 Nov 2005, 22:31, edited 1 time in total.
User avatar
laxieqv
Director
Director
Joined: 24 Sep 2005
Posts: 833
Own Kudos [?]: 1481 [0]
Given Kudos: 0
Send PM
Re: What is the maximum right triangles with legs of length 3 ft [#permalink] New post   05 Nov 2005, 22:02
duttsit wrote:
What is the maximum right triangles with legs of length 3 ft and 4 ft that can be cut from the rectangular sheet of metal of dimension 7 ft x 12 ft.

(A) 7
(B) 8
(C) 10
(D) 12
(E) 14

time: 3 mins for ans with reasons :)


since 14 is the maximum number here and i can show how to cut to get this number. E it is :wink: . Wait, i'm drawing the solution and post here soon.
User avatar
laxieqv
Director
Director
Joined: 24 Sep 2005
Posts: 833
Own Kudos [?]: 1481 [0]
Given Kudos: 0
Send PM
Re: What is the maximum right triangles with legs of length 3 ft [#permalink] New post   05 Nov 2005, 22:10
here it is:
Attachments

proof.doc [24.5 KiB]
Downloaded 101 times

User avatar
duttsit
Senior Manager
Senior Manager
Joined: 22 Aug 2005
Posts: 496
Own Kudos [?]: 660 [0]
Given Kudos: 0
Location: CA
Send PM
Re: What is the maximum right triangles with legs of length 3 ft [#permalink] New post   05 Nov 2005, 22:19
Wonderful lexieqv/tank. Tank i believe you know that, just dividing area gives maximum number of triangles if "there is no leftover". As lexieqv explained in the doc, there is a way to cut. The latter part is more important in this question.
User avatar
tank
Intern
Intern
Joined: 01 Jun 2005
Posts: 17
Own Kudos [?]: 2 [0]
Given Kudos: 0
Send PM
Re: What is the maximum right triangles with legs of length 3 ft [#permalink] New post   05 Nov 2005, 22:30
duttsit wrote:
Wonderful lexieqv/tank. Tank i believe you know that, just dividing area gives maximum number of triangles if "there is no leftover". As lexieqv explained in the doc, there is a way to cut. The latter part is more important in this question.


Ya, luckily in this case, its perfectly divisible.
User avatar
cool_jonny009
Manager
Manager
Joined: 27 Jun 2005
Posts: 241
Own Kudos [?]: 2101 [0]
Given Kudos: 0
Location: MS
Send PM
Re: What is the maximum right triangles with legs of length 3 ft [#permalink] New post   06 Nov 2005, 00:26
duttsit,
I also got E by dividing the area....but if there isleft over ..in the sheet is there any formula or trick to get the # of tringle ..? or drawing the figure is the only hope....:roll:




duttsit wrote:
Wonderful lexieqv/tank. Tank i believe you know that, just dividing area gives maximum number of triangles if "there is no leftover". As lexieqv explained in the doc, there is a way to cut. The latter part is more important in this question.
User avatar
laxieqv
Director
Director
Joined: 24 Sep 2005
Posts: 833
Own Kudos [?]: 1481 [0]
Given Kudos: 0
Send PM
Re: What is the maximum right triangles with legs of length 3 ft [#permalink] New post   06 Nov 2005, 00:49
cool_jonny009 wrote:
duttsit,
I also got E by dividing the area....but if there isleft over ..in the sheet is there any formula or trick to get the # of tringle ..? or drawing the figure is the only hope....:roll:




duttsit wrote:
Wonderful lexieqv/tank. Tank i believe you know that, just dividing area gives maximum number of triangles if "there is no leftover". As lexieqv explained in the doc, there is a way to cut. The latter part is more important in this question.


The trick is that: Firstly you cut triangles from the one width and one length, if there's no overleft, there won't be any overleft.
In this case, 12 is divisible by 4 and 3
7= 3+4
For sure, there won't be any overleft when you cut from one width and one length.
In short, as long as length/width( one of the two) is sum of the triangle's two legs AND width/length( one of the two) is the product of the triangle's two legs, there won't be overleft.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
GMAT Club Bot
gmatclubot
Re: What is the maximum right triangles with legs of length 3 ft [#permalink]
06 Nov 2005, 00:49
Moderators:
Bunuel
Math Expert
92915 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