NEW HERE? LEARN MORE
closeclose
Last visit was: 27 Apr 2024, 12:43 It is currently 27 Apr 2024, 12:43
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

The triangles in the figure above are equilateral and the ratio of the

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
avatar
jimmylow
Manager
Manager
Joined: 31 Oct 2007
Posts: 58
Own Kudos [?]: 135 [24]
Given Kudos: 0
Location: Frankfurt, Germany
Send PM
The triangles in the figure above are equilateral and the ratio of the [#permalink] New post   05 Apr 2008, 22:14
6
Kudos
18
Bookmarks
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

67% (01:51) correct 33% (01:53) wrong based on 776 sessions
Hide Show timer Statistics

The triangles in the figure above are equilateral and the ratio of the length of a side of the larger triangle to the length of a side of the smaller triangle is 2/1. If the area of the larger triangular region is K, what is the area of the shaded region in terms of K?

(A) 3/4*K
(B) 2/3*K
(C) 1/2*K
(D) 1/3*K
(E) 1/4*K

Show Spoiler
Attachment:
2triangles.GIF
2triangles.GIF [ 1.58 KiB | Viewed 27765 times ]
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92955
Own Kudos [?]: 619464 [13]
Given Kudos: 81611
Send PM
CAT Tests Forum Quiz Mode
The triangles in the figure above are equilateral and the ratio of the [#permalink] New post   04 Dec 2010, 04:07
3
Kudos
10
Bookmarks
Expert Reply
jimmylow wrote:


The triangles in the figure above are equilateral and the ratio of the length of a side of the larger triangle to the length of a side of the smaller triangle is 2/1. If the area of the larger triangular region is K, what is the area of the shaded region in terms of K?
(A) 3/4K
(B) 2/3K
(C) 1/2K
(D) 1/3K
(E) 1/4K


Yes, the property given above is very useful. It states: in two similar triangles, the ratio of their areas is the square of the ratio of their sides: \(\frac{AREA}{area}=\frac{S^2}{s^2}\).

As both big and inscribed triangles are equilateral then they are similar, so \(\frac{AREA}{area}=\frac{S^2}{s^2}=\frac{2^2}{1^2}=4\), so if \(AREA=K\) then \(area=\frac{K}{4}\) --> the area of the shaded region equals to \(area_{shaded}=K-\frac{K}{4}=\frac{3K}{4}\).

Answer: A.
User avatar
buffdaddy
Director
Director
Joined: 14 Oct 2007
Posts: 547
Own Kudos [?]: 298 [6]
Given Kudos: 8
Location: Oxford
Schools:Oxford'10
 Q49  V37
Send PM
Re: The triangles in the figure above are equilateral and the ratio of the [#permalink] New post   06 Apr 2008, 08:56
6
Kudos
an easy way to solve this would be to visualise the below triangle instead. it shows u the answer straight away without the need for any calculations
Attachments

trig.JPG
trig.JPG [ 3.86 KiB | Viewed 27201 times ]

General Discussion
User avatar
bkk145
Director
Director
Joined: 10 Jun 2007
Posts: 654
Own Kudos [?]: 1575 [3]
Given Kudos: 0
Send PM
Re: The triangles in the figure above are equilateral and the ratio of the [#permalink] New post   05 Apr 2008, 22:44
2
Kudos
1
Bookmarks
jimmylow wrote:
16. The triangles in the figure above are equilateral and the ratio of the length of a side of the larger triangle to the length of a side of the smaller triangle is 2/1. If the area of the larger triangular region is K, what is the area of the shaded region in terms of K?
(A) 3/4K
(B) 2/3K
(C) 1/2K
(D) 1/3K
(E) 1/4K


A would be my answer.
Area of shaded = Area of Large - Area of Small
Give: Area of Large = K
We need to find Area of Small in term of K.
Triangle area = 1/2 * base * height
and since a side of the large triangle is twice larger than a side of small triangle, we are dealing with (1/2) * (1/2) = 1/4 factor.
Therefore, Area of shaded = K - K/4 = 3K/4
User avatar
sondenso
Director
Director
Joined: 04 May 2006
Posts: 866
Own Kudos [?]: 6811 [0]
Given Kudos: 1
Concentration: Finance
Schools:CBS, Kellogg
Send PM
Re: The triangles in the figure above are equilateral and the ratio of the [#permalink] New post   05 Apr 2008, 22:48
jimmylow wrote:
16. The triangles in the figure above are equilateral and the ratio of the length of a side of the larger triangle to the length of a side of the smaller triangle is 2/1. If the area of the larger triangular region is K, what is the area of the shaded region in terms of K?
(A) 3/4K
(B) 2/3K
(C) 1/2K
(D) 1/3K
(E) 1/4K



A.

the ratio tells you that the larger also is a equilateral triangle.
Length of small one is a
length of larger one is b
a =b/2

the larger arear = K= b^2*(square root(3)/4) I called square root(3)/4 S
the smaller area = a^2 *S = S*b^2 /4 = K/4

the shaded area = K -K/4 =3/4 K
avatar
sixsigma1978
Intern
Intern
Joined: 01 Dec 2010
Posts: 4
Own Kudos [?]: 7 [4]
Given Kudos: 0
Send PM
Re: The triangles in the figure above are equilateral and the ratio of the [#permalink] New post   03 Dec 2010, 13:06
4
Kudos
Another way to do this!
Theorem : If there are Two similar triangles with sides in Ratio : S1 : S2 - then their areas are in the ratio S1^2 : S2 ^2
=> Area of Larger : Area of Smaller = S1^2 : S2^2
=> K : As = 2^2 : 1
=> As = k/4

Therefore, Area of the shaded region : K-K/4 = 3k/4
avatar
gettinit
Manager
Manager
Joined: 13 Jul 2010
Posts: 81
Own Kudos [?]: 218 [0]
Given Kudos: 7
Send PM
Re: The triangles in the figure above are equilateral and the ratio of the [#permalink] New post   06 Dec 2010, 21:28
very useful ratio thanks guys.
User avatar
sanjoo
Senior Manager
Senior Manager
Joined: 06 Aug 2011
Posts: 269
Own Kudos [?]: 596 [1]
Given Kudos: 82
Send PM
Re: The triangles in the figure above are equilateral and the ratio of the [#permalink] New post   18 Oct 2012, 11:08
1
Kudos
m not geting this onne..how K/4??

large triangle have area 4...how k/4?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92955
Own Kudos [?]: 619464 [0]
Given Kudos: 81611
Send PM
CAT Tests Forum Quiz Mode
Re: The triangles in the figure above are equilateral and the ratio of the [#permalink] New post   18 Oct 2012, 11:16
Expert Reply
sanjoo wrote:
m not geting this onne..how K/4??

large triangle have area 4...how k/4?


Check here: the-triangles-in-the-figure-above-are-equilateral-and-the-62201.html#p827422

We have that \(\frac{AREA}{area}=4\). Now, since \(AREA=K\) then \(\frac{K}{area}=4\) --> \(area=\frac{K}{4}\) --> the area of the shaded region equals to \(area_{shaded}=K-\frac{K}{4}=\frac{3K}{4}\).

Hope it's clear.
User avatar
pikachu
Manager
Manager
Joined: 05 Nov 2012
Posts: 55
Own Kudos [?]: 421 [2]
Given Kudos: 8
Concentration: International Business, Operations
Schools: Foster '15 (S)
GPA: 3.65
Send PM
GMAT ToolKit User
Re: The triangles in the figure above are equilateral and the ratio of the [#permalink] New post   09 Jun 2013, 22:14
2
Kudos
jimmylow wrote:
Attachment:
2triangles.GIF
The triangles in the figure above are equilateral and the ratio of the length of a side of the larger triangle to the length of a side of the smaller triangle is 2/1. If the area of the larger triangular region is K, what is the area of the shaded region in terms of K?

(A) 3/4K
(B) 2/3K
(C) 1/2K
(D) 1/3K
(E) 1/4K


The easiest way to solve this one would be by picking numbers. Lets say each side of the larger triangle is 6 and given the ratio 2:1 each side of smaller triangle then is 3. Area of an equilateral triangle can be calculated using formula: \(s^2(\sqrt{3})/4\) where s = side. So area of large triangle = k = \(9(\sqrt{3})\) and area of small triangle = \(9(\sqrt{3})/4\) = \(k/4\). So the area of the smaller triangle is 1/4 the area of the large triangle. Area of shaded region=\(k-k/4\) = \(3/4k\)
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92955
Own Kudos [?]: 619464 [0]
Given Kudos: 81611
Send PM
CAT Tests Forum Quiz Mode
Re: The triangles in the figure above are equilateral and the ratio of the [#permalink] New post   06 Mar 2014, 02:32
Expert Reply
Bumping for review and further discussion.

GEOMETRY: Shaded Region Problems!
User avatar
L
rohit8865
Director
Director
Joined: 05 Mar 2015
Posts: 852
Own Kudos [?]: 861 [0]
Given Kudos: 45
Send PM
Reviews Badge
Re: The triangles in the figure above are equilateral and the ratio of the [#permalink] New post   20 Jul 2016, 11:37
Bunuel wrote:
Bumping for review and further discussion.

GEOMETRY: Shaded Region Problems!

Let side of larger eq. triangle=2X
area=sq.root3/4*(2X)^2------->sq.root3*x^2------(A)
therefore side of smaller eq. triangle=X(given ratio=2/1)
area of smaller- sq.root3*x^2/4
area of shaded part=larger-smaller triangle
=sq.root3*x^2-sq.root3*x^2/4------------>sq.root3*x^2(1-1/4)
substituting from eq. (A)
area of shaded part=3/4K
Ans A
User avatar
G
KanishkM
Director
Director
Joined: 09 Mar 2018
Posts: 783
Own Kudos [?]: 453 [0]
Given Kudos: 123
Location: India
Schools: DeGroote'21 Desautels '21 NUS '21
Send PM
Re: The triangles in the figure above are equilateral and the ratio of the [#permalink] New post   11 Feb 2019, 03:04
jimmylow wrote:
Attachment:
2triangles.GIF
The triangles in the figure above are equilateral and the ratio of the length of a side of the larger triangle to the length of a side of the smaller triangle is 2/1. If the area of the larger triangular region is K, what is the area of the shaded region in terms of K?

(A) 3/4K
(B) 2/3K
(C) 1/2K
(D) 1/3K
(E) 1/4K


KeyWord: Be careful of such questions

area of the shaded region in terms of K

Nothing much is to be done here

ratio of the length of a side of the larger triangle to the length of a side of the smaller triangle is 2/1 => 6/3

Area of bigger triangle => root3/4 * 36 = k -----(a)

Area of smaller triangle => root3/4 * 9 = k' --------(b)

divide (a) by (b)

k/k' = 4/1

k/4 = k'

Now what needs to be find ???

area of the shaded region in terms of K = 1 - k/4 = 3k/4

A
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14830
Own Kudos [?]: 64952 [0]
Given Kudos: 427
Location: Pune, India
Send PM
Re: The triangles in the figure above are equilateral and the ratio of the [#permalink] New post   11 Feb 2019, 04:09
Expert Reply
jimmylow wrote:
Attachment:
2triangles.GIF
The triangles in the figure above are equilateral and the ratio of the length of a side of the larger triangle to the length of a side of the smaller triangle is 2/1. If the area of the larger triangular region is K, what is the area of the shaded region in terms of K?

(A) 3/4K
(B) 2/3K
(C) 1/2K
(D) 1/3K
(E) 1/4K


All Equilateral triangles are similar by AA.
And we know this about similar triangles - the ratio of their areas will be square of the ratio of their sides.
This is discussed here: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/03 ... -the-gmat/

So if the ratio of their sides is 2/1, the ratio of their areas will be 4/1.

So area of smaller triangle is 1/4 of larger triangle. The area of the rest of the larger triangle will be (3/4)K.

Answer (A)
User avatar
L
Kushchokhani
Director
Director
Joined: 05 Jan 2020
Status:Admitted to IIM Shillong (PGPEx 2023-24)
Affiliations: CFA Institute; ICAI; BCAS
Posts: 588
Own Kudos [?]: 554 [1]
Given Kudos: 694
Location: India
WE 2: EA to CFO (Consumer Products)
GPA: 3.78
WE:Corporate Finance (Commercial Banking)
Send PM
Reviews Badge CAT Tests Forum Quiz Mode
Re: The triangles in the figure above are equilateral and the ratio of the [#permalink] New post   29 May 2022, 08:04
1
Kudos
Bunuel wrote:
Bumping for review and further discussion.

GEOMETRY: Shaded Region Problems!

Bunuel

Link's post deleted?
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92955
Own Kudos [?]: 619464 [0]
Given Kudos: 81611
Send PM
CAT Tests Forum Quiz Mode
Re: The triangles in the figure above are equilateral and the ratio of the [#permalink] New post   29 May 2022, 08:07
Expert Reply
Kushchokhani wrote:
Bunuel wrote:
Bumping for review and further discussion.

GEOMETRY: Shaded Region Problems!

Bunuel

Link's post deleted?


Updated the link: GEOMETRY: Shaded Region Problems!

Thank you very much! :thumbsup:
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32717
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: The triangles in the figure above are equilateral and the ratio of the [#permalink] New post   15 Jul 2023, 08:48
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.
GMAT Club Bot
gmatclubot
Re: The triangles in the figure above are equilateral and the ratio of the [#permalink]
15 Jul 2023, 08:48
Moderators:
Bunuel
Math Expert
92955 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