NEW HERE? LEARN MORE
closeclose
Last visit was: 27 Apr 2024, 13:20 It is currently 27 Apr 2024, 13:20
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 triangle ABC is the equilateral triangle. Moreover, AB, BC, and AC

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
MathRevolution
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10161
Own Kudos [?]: 16609 [9]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
The triangle ABC is the equilateral triangle. Moreover, AB, BC, and AC [#permalink] New post   12 Nov 2019, 00:39
2
Kudos
6
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

70% (02:28) correct 30% (02:11) wrong based on 154 sessions
Hide Show timer Statistics
[GMAT math practice question]

Attachment:
11.12ps.png
11.12ps.png [ 23.02 KiB | Viewed 2732 times ]


(geometry) The triangle \(ABC\) is the equilateral triangle. Moreover, \(AB, BC\), and \(AC\) are parallel to \(n, l,\) and \(m,\) respectively. As the figure shows, \(DI = 3, EF = 2, FG = 6\) and \(HG = 1.\) What is \(x + y\)?

A. \(6\)

B. \(7\)

C. \(8\)

D. \(9\)

E. \(10\)
ShowHide Answer
Official Answer
D
User avatar
L
MathRevolution
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10161
Own Kudos [?]: 16609 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: The triangle ABC is the equilateral triangle. Moreover, AB, BC, and AC [#permalink] New post   14 Nov 2019, 01:26
1
Kudos
Expert Reply
=>

Since triangles \(ADI, BEF\) and \(CGH\) are equilateral triangles, \(AD = AI = 3, BE = BF = 2\) and \(CG = CH = 1\).

Then we have \(3 + x + 1 = 3 + y + 2 = 2 + 6 + 1\), since we have \(AB = BC = CA\), which simplifies to \(x + 4 = y + 5 = 9.\)

So we have \(x = 5, y = 4\) and \(x + y = 9.\)

Therefore, D is the answer.
Answer: D
User avatar
P
Blair15
Manager
Manager
Joined: 07 Oct 2020
Posts: 157
Own Kudos [?]: 121 [1]
Given Kudos: 217
Location: India
GMAT 1: 630 Q46 V31
Send PM
Re: The triangle ABC is the equilateral triangle. Moreover, AB, BC, and AC [#permalink] New post   31 Aug 2022, 06:26
1
Kudos
MathRevolution wrote:
=>

Since triangles \(ADI, BEF\) and \(CGH\) are equilateral triangles, \(AD = AI = 3, BE = BF = 2\) and \(CG = CH = 1\).

Then we have \(3 + x + 1 = 3 + y + 2 = 2 + 6 + 1\), since we have \(AB = BC = CA\), which simplifies to \(x + 4 = y + 5 = 9.\)

So we have \(x = 5, y = 4\) and \(x + y = 9.\)

Therefore, D is the answer.
Answer: D



Hey, why are triangles ADI, BEF, CGH equilateral triangles?
User avatar
B
asterisk357
Intern
Intern
Joined: 19 Sep 2020
Posts: 11
Own Kudos [?]: 20 [0]
Given Kudos: 170
Location: India
Concentration: General Management, Technology
WE:Information Technology (Consulting)
Send PM
Re: The triangle ABC is the equilateral triangle. Moreover, AB, BC, and AC [#permalink] New post   19 Sep 2022, 12:34
Blair15 wrote:
MathRevolution wrote:
=>

Since triangles \(ADI, BEF\) and \(CGH\) are equilateral triangles, \(AD = AI = 3, BE = BF = 2\) and \(CG = CH = 1\).

Then we have \(3 + x + 1 = 3 + y + 2 = 2 + 6 + 1\), since we have \(AB = BC = CA\), which simplifies to \(x + 4 = y + 5 = 9.\)

So we have \(x = 5, y = 4\) and \(x + y = 9.\)

Therefore, D is the answer.
Answer: D



Hey, why are triangles ADI, BEF, CGH equilateral triangles?


Blair15
Consider triangle ADI and triangle ABC
Angle A is common in both triangles
Since DI is || BC, angle B= angle D and angle C= angle (corresponding angles)
Since all three angles are same, the two triangles are similar.
User avatar
P
Blair15
Manager
Manager
Joined: 07 Oct 2020
Posts: 157
Own Kudos [?]: 121 [0]
Given Kudos: 217
Location: India
GMAT 1: 630 Q46 V31
Send PM
Re: The triangle ABC is the equilateral triangle. Moreover, AB, BC, and AC [#permalink] New post   19 Sep 2022, 12:45
asterisk357 wrote:
Blair15 wrote:
MathRevolution wrote:
=>

Since triangles \(ADI, BEF\) and \(CGH\) are equilateral triangles, \(AD = AI = 3, BE = BF = 2\) and \(CG = CH = 1\).

Then we have \(3 + x + 1 = 3 + y + 2 = 2 + 6 + 1\), since we have \(AB = BC = CA\), which simplifies to \(x + 4 = y + 5 = 9.\)

So we have \(x = 5, y = 4\) and \(x + y = 9.\)

Therefore, D is the answer.
Answer: D



Hey, why are triangles ADI, BEF, CGH equilateral triangles?


Blair15
Consider triangle ADI and triangle ABC
Angle A is common in both triangles
Since DI is || BC, angle B= angle D and angle C= angle (corresponding angles)
Since all three angles are same, the two triangles are similar.


So if a triangle is similar to an equilateral triangle, it makes the other triangle equilateral too?
User avatar
B
asterisk357
Intern
Intern
Joined: 19 Sep 2020
Posts: 11
Own Kudos [?]: 20 [1]
Given Kudos: 170
Location: India
Concentration: General Management, Technology
WE:Information Technology (Consulting)
Send PM
The triangle ABC is the equilateral triangle. Moreover, AB, BC, and AC [#permalink] New post   19 Sep 2022, 13:16
1
Kudos
Hey, why are triangles ADI, BEF, CGH equilateral triangles?[/quote]

Blair15
Consider triangle ADI and triangle ABC
Angle A is common in both triangles
Since DI is || BC, angle B= angle D and angle C= angle (corresponding angles)
Since all three angles are same, the two triangles are similar.[/quote]

So if a triangle is similar to an equilateral triangle, it makes the other triangle equilateral too?[/quote]

Yes. The ratio of the corresponding sides are equal.
[Refer attachment]
Assume if the triangles are equilateral.
Assuming AB=5, then BC=5
5/DE=5/EF=5/DF
DE=EF=DF

Apply same method to this question
Attachments

Untitled.png
Untitled.png [ 61.59 KiB | Viewed 952 times ]

GMAT Club Bot
gmatclubot
The triangle ABC is the equilateral triangle. Moreover, AB, BC, and AC [#permalink]
19 Sep 2022, 13:16
Moderators:
Bunuel
Math Expert
92956 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