Find all School-related info fast with the new School-Specific MBA Forum

It is currently 27 Aug 2014, 11:13

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

there are two triangles whose three vertices have same

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 30 Oct 2007
Posts: 9
Followers: 0

Kudos [?]: 0 [0], given: 0

there are two triangles whose three vertices have same [#permalink] New post 02 Nov 2007, 16:49
there are two triangles whose three vertices have same angles (x, y, z). If area of one triangle is twice the area of the other triangle, and the base of the smaller triangle is s, and base of the larger triangle is S, then what is S, in terms of s?

√2/2 s
√3/2 s
√2 s
√3 s
2 s

Last edited by iwo on 02 Nov 2007, 18:08, edited 1 time in total.
Director
Director
avatar
Joined: 11 Jun 2007
Posts: 932
Followers: 1

Kudos [?]: 45 [0], given: 0

GMAT Tests User
Re: triangles question- seems hard [#permalink] New post 02 Nov 2007, 17:12
iwo wrote:
there are two triangles whose vertices have same angles. If area of one triangle is twice the area of the other triangle, and the base of the smaller triangle is s, and base of the larger triangle is S, then what is S, in terms of s?

√2/2 s
√3/2 s
√2 s
√3 s
2 s


vertices have same angles <-- that tells us we are dealing with equilateral triangles with 60 degrees for each angle, so the height will be split with the 30-60-90 degree and will be 1/2*base* √3

i get A (although not 100% sure) please confirm

so lets start with the larger triangle
area = 1/2bh, stem tells us base is big S
area = 1/2 S * (√3)/2 S

smaller triangle
area = 1/2bh, base is little s
area = 1/2 s * (√3)/2 s

since area for larger triangle is twice that of the smaller
than S * (√3)/2S = 1/2 s * (√3)/2s

solving for S (multiply inverse 2/√3 on both sides to clear LHS)

S^2 = √3/4 s^2 * 2/√3
S^2 = s^2 * 2/4
and take the sqrt on both sides:
S = s * √(1/2)
S = s * √2/2
Intern
Intern
avatar
Joined: 30 Oct 2007
Posts: 9
Followers: 0

Kudos [?]: 0 [0], given: 0

 [#permalink] New post 02 Nov 2007, 18:06
nope thats not the OA

both triangles have same angles x-y-z, no degrees are given, sorry i forgot to mention that
Director
Director
avatar
Joined: 11 Jun 2007
Posts: 932
Followers: 1

Kudos [?]: 45 [0], given: 0

GMAT Tests User
 [#permalink] New post 02 Nov 2007, 18:21
iwo wrote:
nope thats not the OA

both triangles have same angles x-y-z, no degrees are given, sorry i forgot to mention that


duh!!! sorry i know where i screwed up (hope not on test day)

continuation...

since area for larger triangle is twice that of the smaller
than S * √3/4S = 2* (s * √3/4s)

solving for S (multiply inverse 4/√3 on both sides to clear LHS)

S^2 = √3/2 s^2 * 4/√3
S^2 = s^2 * 4/2
and take the sqrt on both sides:
S = s * √2
so the third choice.. . is that correct?
Director
Director
avatar
Joined: 09 Aug 2006
Posts: 767
Followers: 1

Kudos [?]: 46 [0], given: 0

GMAT Tests User
Re: triangles question- seems hard [#permalink] New post 02 Nov 2007, 22:53
iwo wrote:
there are two triangles whose three vertices have same angles (x, y, z). If area of one triangle is twice the area of the other triangle, and the base of the smaller triangle is s, and base of the larger triangle is S, then what is S, in terms of s?

√2/2 s
√3/2 s
√2 s
√3 s
2 s


Getting C.

The ratio of the area of similar triangles is the square of the ratio of similar sides.

Since all three angles are equal the 2 triangles are similar.

Ratio of ar. of small triangle : ratio of ar. of big triangle = 1:2
Therefore, ratio of sides of small triangle : ratio of sides of big triangle = 1 : sqrt(2)

If s = 1 then S = sqrt(2)s
Re: triangles question- seems hard   [#permalink] 02 Nov 2007, 22:53
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic Two isosceles Triangles have equal vertical angles and their vomhorizon 5 15 Nov 2012, 06:39
1 If vertices of a triangle have coordinates (-2, 2), swatirpr 4 10 Dec 2009, 12:42
Vertices of a triangle have coordinates , , and . Is the arjtryarjtry 3 07 Sep 2008, 22:58
A scalene triangle is a triangle whose three sides are of kevincan 8 30 Jul 2006, 01:10
Find the area of the triangle whose vertices are (-6, -2), revital 4 28 Nov 2004, 06:08
Display posts from previous: Sort by

there are two triangles whose three vertices have same

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.