In the figures above, if the area of the triangle on the right is twic : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 18 Jan 2017, 10:23

# STARTING SOON:

Open Admission Chat with MBA Experts of Personal MBA Coach - Join Chat Room to Participate.

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In the figures above, if the area of the triangle on the right is twic

Author Message
TAGS:

### Hide Tags

Intern
Joined: 08 Mar 2010
Posts: 20
Schools: Richard Ivey School of Business (University of Western Ontario)
Followers: 0

Kudos [?]: 58 [0], given: 0

In the figures above, if the area of the triangle on the right is twic [#permalink]

### Show Tags

08 Mar 2010, 10:02
2
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

61% (02:14) correct 39% (01:46) wrong based on 65 sessions

### HideShow timer Statistics

In the figures above, if the area of the triangle on the right is twice the area of the triangle on the left, then in terms of s, S=

A. $$\frac{\sqrt{2}}{2}s$$

B. $$\frac{\sqrt{3}}{2}s$$

C. $$\sqrt{2}s$$

D. $$\sqrt{3}s$$

E. $$2s$$

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-figures-above-if-the-area-of-the-triangle-on-the-128929.html

[Reveal] Spoiler:
Attachment:

Untitled.jpg [ 8.32 KiB | Viewed 2565 times ]
[Reveal] Spoiler: OA
Manager
Joined: 10 Aug 2009
Posts: 123
Followers: 3

Kudos [?]: 16 [0], given: 13

Re: In the figures above, if the area of the triangle on the right is twic [#permalink]

### Show Tags

08 Mar 2010, 12:02
seems easy enough....

for similar triangles (all angles the same) the following holds:

(area A)/(area b) = ( x/y )^2 (where x and y are corresponding lengths)

in this case, let A be the area of the smaller triangle. We have:

2A/A = (S/s)^2 => S/s = 2^0.5
S = s*2^0.5
Intern
Joined: 03 Nov 2009
Posts: 21
Location: New York, New York
Followers: 0

Kudos [?]: 5 [1] , given: 1

Re: In the figures above, if the area of the triangle on the right is twic [#permalink]

### Show Tags

08 Mar 2010, 12:18
1
KUDOS
For Small triangle, lets say h is the height. And for the big triangle, H is the height.
Area = 1/2 (s*h)
Area = 1/2 (S*H)

According to the info in the question -->
1/2 (S*H) = 2 * [1/2 (s*h)]
= s*h
=> s = S*H/2h
=> h/H = S/2s ----------------------1

For similar triangles
h/H = s/S -----------------------2

put 2 in 1 ==>
s/S = S/2s
=> s^2 = S^2/2
= sqrt(2).s = S

_________________

--------------------------
http://gmatmbablog.co.nr/
--------------------------

Senior Manager
Joined: 13 Dec 2009
Posts: 263
Followers: 10

Kudos [?]: 184 [0], given: 13

Re: In the figures above, if the area of the triangle on the right is twic [#permalink]

### Show Tags

15 Mar 2010, 08:29
With the property ratio of area in similar triangle = (ratio of any similar side)^2
so s/S = sqrt(1/2) => S = s*sqrt(2) hence C is the answer
_________________

My debrief: done-and-dusted-730-q49-v40

Manager
Joined: 18 Feb 2010
Posts: 174
Schools: ISB
Followers: 8

Kudos [?]: 199 [0], given: 0

Re: In the figures above, if the area of the triangle on the right is twic [#permalink]

### Show Tags

20 Mar 2010, 08:01
nickk wrote:
seems easy enough....

for similar triangles (all angles the same) the following holds:

(area A)/(area b) = ( x/y )^2 (where x and y are corresponding lengths)

in this case, let A be the area of the smaller triangle. We have:

2A/A = (S/s)^2 => S/s = 2^0.5
S = s*2^0.5

Where does this property comes from??
_________________

CONSIDER AWARDING KUDOS IF MY POST HELPS !!!

Senior Manager
Joined: 13 Dec 2009
Posts: 263
Followers: 10

Kudos [?]: 184 [0], given: 13

Re: In the figures above, if the area of the triangle on the right is twic [#permalink]

### Show Tags

21 Mar 2010, 11:10
mustdoit wrote:
nickk wrote:
seems easy enough....

for similar triangles (all angles the same) the following holds:

(area A)/(area b) = ( x/y )^2 (where x and y are corresponding lengths)

in this case, let A be the area of the smaller triangle. We have:

2A/A = (S/s)^2 => S/s = 2^0.5
S = s*2^0.5

Where does this property comes from??

This is the similar trianlges property. Any two triangles are similar if they have same corresponding angles or if the ratio of their corresponding sides are same.
In case two triangles are similar, ratio of their areas = (ratio of side)^2
_________________

My debrief: done-and-dusted-730-q49-v40

Director
Joined: 03 Sep 2006
Posts: 879
Followers: 6

Kudos [?]: 769 [0], given: 33

### Show Tags

06 May 2010, 11:34
Attachments

PS4.PNG [ 20.63 KiB | Viewed 3203 times ]

Math Expert
Joined: 02 Sep 2009
Posts: 36545
Followers: 7076

Kudos [?]: 93089 [4] , given: 10542

### Show Tags

06 May 2010, 12:05
4
KUDOS
Expert's post
3
This post was
BOOKMARKED
LM wrote:
In the figures above, if the area of the triangle on the right is twice the area of the triangle on the left, then in terms of s, S=

Property of similar triangles: In two similar triangles, the ratio of their areas is the square of the ratio of their sides.

Hence $$\frac{AREA}{area}=\frac{S^2}{s^2}=2$$ --> $$S=s\sqrt{2}$$.

_________________
Director
Joined: 03 Sep 2006
Posts: 879
Followers: 6

Kudos [?]: 769 [0], given: 33

### Show Tags

06 May 2010, 12:34
Bunuel wrote:
LM wrote:

Property of similar triangles: In two similar triangles, the ratio of their areas is the square of the ratio of their sides.

Hence $$\frac{AREA}{area}=\frac{S^2}{s^2}=2$$ --> $$S=s\sqrt{2}$$.

Thanks I did not know this! the ratio of their areas is the square of the ratio of their sides.
Manager
Status: Last few days....Have pressed the throttle
Joined: 20 Jun 2010
Posts: 70
WE 1: 6 years - Consulting
Followers: 3

Kudos [?]: 46 [0], given: 27

### Show Tags

25 Aug 2010, 01:24
Bunuel that was awesome...although read all concepts in your Polygon blog..but did not click to me. +1 to you as always
_________________

Consider giving Kudos if my post helps in some way

Manager
Joined: 19 Apr 2010
Posts: 210
Schools: ISB, HEC, Said
Followers: 4

Kudos [?]: 77 [0], given: 28

### Show Tags

08 Sep 2010, 05:39
This is certainly not a 700 Level question Bunuel can be moved
Intern
Joined: 06 Sep 2010
Posts: 17
Schools: HBS
WE 1: Management Consulting- 2 years
WE 2: Private Equity- 2 years
Followers: 1

Kudos [?]: 72 [0], given: 6

### Show Tags

06 Oct 2010, 05:29
I eliminated A and B for this because I knew that S had to be greater than s, but I did not know how to find the exact answer. I also eliminated 2s because that excludes the height when calculating area, but again I could not figure out how to get the exact answer. Any help please?? Thanks!!! The file is attached.

Jeremiah
Attachments

Geo PS1.docx [57.39 KiB]

Math Expert
Joined: 02 Sep 2009
Posts: 36545
Followers: 7076

Kudos [?]: 93089 [1] , given: 10542

### Show Tags

06 Oct 2010, 05:39
1
KUDOS
Expert's post
Merging similar topics.
_________________
Intern
Joined: 08 Oct 2009
Posts: 12
Followers: 0

Kudos [?]: 11 [0], given: 3

### Show Tags

23 Oct 2010, 09:08
If you don't know the property:
take H=height of the larger triangle
and h=height of the smaller triangle

As the area is twice ,so HS=2hs
because triangles are similar h/s=H/S or h/H=s/S

Now after solving we get S=(2^1/2)s
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13437
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: In the figures above, if the area of the triangle on the right is twic [#permalink]

### Show Tags

05 May 2016, 06:06
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 36545
Followers: 7076

Kudos [?]: 93089 [0], given: 10542

Re: In the figures above, if the area of the triangle on the right is twic [#permalink]

### Show Tags

05 May 2016, 06:50
ronny13 wrote:

In the figures above, if the area of the triangle on the right is twice the area of the triangle on the left, then in terms of s, S=

A. $$\frac{\sqrt{2}}{2}s$$

B. $$\frac{\sqrt{3}}{2}s$$

C. $$\sqrt{2}s$$

D. $$\sqrt{3}s$$

E. $$2s$$

Since in the given triangles the three angles are identical then they are similar triangles.

Useful property of similar triangles: in two similar triangles, the ratio of their areas is the square of the ratio of their sides.

Hence $$\frac{AREA}{area}=\frac{S^2}{s^2}=2$$ --> $$S=s\sqrt{2}$$.

For more on this subject check Triangles chapter of Math Book: math-triangles-87197.html

Hope it helps.

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-the-figures-above-if-the-area-of-the-triangle-on-the-128929.html
_________________
Re: In the figures above, if the area of the triangle on the right is twic   [#permalink] 05 May 2016, 06:50
Similar topics Replies Last post
Similar
Topics:
1 In the figure above, the base of the uniform solid is a right triangle 2 29 Dec 2015, 06:55
7 What is the area of the triangle in the figure above? 2 27 Dec 2015, 09:42
4 In the figure above, a circle is inscribed in a right triangle. If 3 21 Jul 2015, 02:14
5 In the figures above, if the area of the triangle on the 7 12 Mar 2012, 01:44
3 In the figure above, if the area of the triangle on he right 10 02 Dec 2007, 07:00
Display posts from previous: Sort by