NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 17:07 It is currently 26 Apr 2024, 17:07
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

In the figure above, triangle abc is similar to triangle ABC. X, Y, Z

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 [?]: 619244 [16]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
In the figure above, triangle abc is similar to triangle ABC. X, Y, Z [#permalink] New post   06 Jun 2017, 10:25
4
Kudos
12
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

64% (01:32) correct 36% (01:59) wrong based on 297 sessions
Hide Show timer Statistics

In the figure above, triangle abc is similar to triangle ABC. X, Y, Z and x, y, z represent the sides of each similar triangle. If the area of triangle ABC is twice the area of triangle abc, which of the following expresses X in terms of x?

A. \(\frac{x}{\sqrt{2}}\)

B. \(x\sqrt{2}\)

C. x/2

D. 2x

E. 4x

Show Spoiler
Attachment:
SimilarABC.png
SimilarABC.png [ 10.2 KiB | Viewed 8186 times ]
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
S
quantumliner
Senior Manager
Senior Manager
Joined: 24 Apr 2016
Posts: 255
Own Kudos [?]: 682 [9]
Given Kudos: 48
Send PM
Re: In the figure above, triangle abc is similar to triangle ABC. X, Y, Z [#permalink] New post   06 Jun 2017, 11:14
3
Kudos
6
Bookmarks
Let area of Triangle abc = a
Let area of Triangle ABC = 2a

As triangles ABC and abc are similar, then

\(\frac{Area of Triangle ABC}{Area of Triangle ABC}\) = \(X^2\)/\(x^2\)

\(\frac{2a}{a}\) = \(X^2\)/\(x^2\)

Simplifying the above we get,

\(\frac{X}{x}\)=\(\sqrt{2}\)

X = x\(\sqrt{2}\)

Answer is B
General Discussion
avatar
B
KHow
Intern
Intern
Joined: 15 Nov 2017
Posts: 44
Own Kudos [?]: 13 [0]
Given Kudos: 182
Send PM
Re: In the figure above, triangle abc is similar to triangle ABC. X, Y, Z [#permalink] New post   12 Jan 2019, 15:33
Thank you for your explanation! I am a little bit confused about how we know the ratio for this triangle is 1:1:sqrt2. Could you explain in more detail how you got this answer? Thank you very much! :)
quantumliner wrote:
Let area of Triangle abc = a
Let area of Triangle ABC = 2a

As triangles ABC and abc are similar, then

\(\frac{Area of Triangle ABC}{Area of Triangle ABC}\) = \(X^2\)/\(x^2\)

\(\frac{2a}{a}\) = \(X^2\)/\(x^2\)

Simplifying the above we get,

\(\frac{X}{x}\)=\(\sqrt{2}\)

X = x\(\sqrt{2}\)

Answer is B
User avatar
G
MBAnBConsulting
Manager
Manager
Joined: 23 Apr 2016
Status:MBA Admissions Consultant
Affiliations: MBA and Beyond
Posts: 178
Own Kudos [?]: 57 [0]
Given Kudos: 80
Location: Singapore
Shantanu: Sharma
Concentration: Entrepreneurship, Technology
Schools: INSEAD Jan '17 (A)
WE:Other (Internet and New Media)
Send PM
Re: In the figure above, triangle abc is similar to triangle ABC. X, Y, Z [#permalink] New post   13 Jan 2019, 04:20
KHow,

Ratio of all the similar sides of XYZ to xyz is Sqrt 2.
X/x = Y/y = Z/z = Sqrt 2

Let me know if you got it.

Cheers!
Shantanu Sharma
INSEAD Class of December 2017
MBA and Beyond Consulting

KHow wrote:
Thank you for your explanation! I am a little bit confused about how we know the ratio for this triangle is 1:1:sqrt2. Could you explain in more detail how you got this answer? Thank you very much! :)
quantumliner wrote:
Let area of Triangle abc = a
Let area of Triangle ABC = 2a

As triangles ABC and abc are similar, then

\(\frac{Area of Triangle ABC}{Area of Triangle ABC}\) = \(X^2\)/\(x^2\)

\(\frac{2a}{a}\) = \(X^2\)/\(x^2\)

Simplifying the above we get,

\(\frac{X}{x}\)=\(\sqrt{2}\)

X = x\(\sqrt{2}\)

Answer is B
avatar
B
dcwanderer30
Intern
Intern
Joined: 09 Mar 2017
Posts: 9
Own Kudos [?]: 1 [0]
Given Kudos: 23
Send PM
Re: In the figure above, triangle abc is similar to triangle ABC. X, Y, Z [#permalink] New post   13 Jan 2019, 11:27
quantumliner wrote:
Let area of Triangle abc = a
Let area of Triangle ABC = 2a

As triangles ABC and abc are similar, then

\(\frac{Area of Triangle ABC}{Area of Triangle ABC}\) = \(X^2\)/\(x^2\)

\(\frac{2a}{a}\) = \(X^2\)/\(x^2\)

Simplifying the above we get,

\(\frac{X}{x}\)=\(\sqrt{2}\)

X = x\(\sqrt{2}\)

Answer is B


Why is the area of Triangle ABC/Triangle abc = X^2/x^2? Where are the squares coming from?
avatar
B
Pranjal3107
Current Student
Joined: 13 Apr 2020
Posts: 150
Own Kudos [?]: 18 [0]
Given Kudos: 1711
Location: India
Schools: NTU (A) ISB '23 (D)
GMAT 1: 710 Q45 V41
GPA: 3
Send PM
Re: In the figure above, triangle abc is similar to triangle ABC. X, Y, Z [#permalink] New post   25 Sep 2020, 09:06
dcwanderer30 wrote:
quantumliner wrote:
Let area of Triangle abc = a
Let area of Triangle ABC = 2a

As triangles ABC and abc are similar, then

\(\frac{Area of Triangle ABC}{Area of Triangle ABC}\) = \(X^2\)/\(x^2\)

\(\frac{2a}{a}\) = \(X^2\)/\(x^2\)

Simplifying the above we get,

\(\frac{X}{x}\)=\(\sqrt{2}\)

X = x\(\sqrt{2}\)

Answer is B


Why is the area of Triangle ABC/Triangle abc = X^2/x^2? Where are the squares coming from?



Hi ! is there some kind of rule for X^2/x^2 for similar triangles ?
User avatar
L
Fdambro294
VP
VP
Joined: 10 Jul 2019
Posts: 1392
Own Kudos [?]: 542 [3]
Given Kudos: 1656
Send PM
Re: In the figure above, triangle abc is similar to triangle ABC. X, Y, Z [#permalink] New post   25 Sep 2020, 23:50
2
Kudos
1
Bookmarks
Since we are given that the 2 Triangles are Similar, the Ratio of the Similar Triangles Area:


Area ABC / Area abc = 2 / 1


Ratio of the Corresponding Sides of the 2 Triangles will be in the Ratio that is the square root of the Area Ratio in its most simplified Form


Side ABC / Side abc = sqrt(2) / sqrt(1)


Side X on Triangle ABC Corresponds to Side x on Triangle abc. The 2 Sides will be in the Side Ratio given above.


Side ABC / Side abc = sqrt(2) / 1 = X / x


X = "in terms of x" = sqrt(2) * x

-B-
User avatar
D
BrushMyQuant
Tutor
Joined: 05 Apr 2011
Status:Tutor - BrushMyQuant
Posts: 1777
Own Kudos [?]: 2094 [0]
Given Kudos: 100
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Send PM
Re: In the figure above, triangle abc is similar to triangle ABC. X, Y, Z [#permalink] New post   24 Jan 2023, 07:57
Expert Reply
Top Contributor
↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧




Theory: If Two Triangles are Similar then ratio of their Areas is equal to square of ratio of their sides

Given that △ abc and △ ABC are similar and the area of △ ABC is twice the area of △ abc.

=> \(\frac{Area Of △ ABC }{ Area Of △ abc} = (\frac{X }{ x})^2\)
=> \(\frac{2 * Area Of △ abc }{ Area Of △ abc} = (\frac{X }{ x})^2\)
=> \(\frac{X }{ x}\) = \(\sqrt{2}\)
=> X = x * \(\sqrt{2}\)

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Similar Triangles

GMAT Club Bot
gmatclubot
Re: In the figure above, triangle abc is similar to triangle ABC. X, Y, Z [#permalink]
24 Jan 2023, 07:57
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