GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 15 Nov 2019, 06:37

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.

Close

Request Expert Reply

Confirm Cancel

The height of an equilateral triangle is the side of a smaller equilat

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59073
The height of an equilateral triangle is the side of a smaller equilat  [#permalink]

Show Tags

New post 07 Sep 2016, 04:44
2
11
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

66% (02:28) correct 34% (02:19) wrong based on 174 sessions

HideShow timer Statistics

Image
The height of an equilateral triangle is the side of a smaller equilateral triangle, as shown above. If the side of the large equilateral triangle is 1, what is AB?

A. 1 - √3/2
B. 0.25
C. 2 - √3
D. 1/3
E. 1 - √3/4

Attachment:
T6036.png
T6036.png [ 7.15 KiB | Viewed 10341 times ]

_________________
Most Helpful Expert Reply
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4063
Location: Canada
The height of an equilateral triangle is the side of a smaller equilat  [#permalink]

Show Tags

New post Updated on: 31 Oct 2019, 07:38
8
Top Contributor
3
Bunuel wrote:
Image
The height of an equilateral triangle is the side of a smaller equilateral triangle, as shown above. If the side of the large equilateral triangle is 1, what is AB?

A. 1 - √3/2
B. 0.25
C. 2 - √3
D. 1/3
E. 1 - √3/4

Attachment:
T6036.png


The length of one side of the large equilateral triangle is 1...
Image

The line representing the height of that triangle will cut that side in half, which means the one side (indicated below) will have length 1/2
Image

Next, since the smaller triangle (in blue below) is also an equilateral triangle, each angle in that triangle is 60 degrees.
Image

This means the angle adjacent to the 60 degree angle must be 30 degrees....
Image

Also, since the bigger triangle (in red below) is an equilateral triangle, each angle in that triangle is 60 degrees.
Image

Now let's focus our attention on the small red triangle (below)
Image

Since we know 2 of the angles in the triangle, we can see that the 3rd angle is 90 degrees.
Image

This small red triangle is a SPECIAL 30-60-90 triangle, and when we compare it to our "base" 30-60-90 triangle (in blue below), we see that the side opposite the 90-degree angle has length 2 in the base triangle, and the same corresponding side in the red triangle has length 1/2
Image

This tells us that the red triangle is 1/4 the size of the blue base triangle.
So, since the side opposite the 30-degree angle has length 1 in the base triangle, and the length of the corresponding side in the red triangle = 1(1/4) = 1/4
Image

Answer:

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image

Originally posted by GMATPrepNow on 09 Sep 2016, 12:09.
Last edited by GMATPrepNow on 31 Oct 2019, 07:38, edited 1 time in total.
General Discussion
Intern
Intern
avatar
Joined: 17 Mar 2013
Posts: 6
Re: The height of an equilateral triangle is the side of a smaller equilat  [#permalink]

Show Tags

New post 07 Sep 2016, 20:14
2
the height of the equilateral triangle is also perpendicular bisector for the larger equilateral triangle. So it cuts the side into half. so its 0.5. smaller triangle is equilateral so one of the angle is 60. the other angle would be 180-(90+60) = 30. smaller triangle ABX is 30-60-90 triangle so the side AB will be 0.25.
Retired Moderator
avatar
G
Joined: 26 Nov 2012
Posts: 555
The height of an equilateral triangle is the side of a smaller equilat  [#permalink]

Show Tags

New post 07 Sep 2016, 06:38
1
Bunuel wrote:
Image
The height of an equilateral triangle is the side of a smaller equilateral triangle, as shown above. If the side of the large equilateral triangle is 1, what is AB?

A. 1 - √3/2
B. 0.25
C. 2 - √3
D. 1/3
E. 1 - √3/4

Attachment:
T6036.png


Height of equilateral triangle is √3/2(a)

Given side of larger triangle is a = 1 then height of larger triangle then height is √3/2(1) = √3/2 and this is side of smaller equilateral triangle.

We have side of smaller triangle and height of smaller triangle is √3/2(a) => √3/2(√3/2) = 3/4.

We have height of smaller triangle.

AB is on larger equilateral triangle and we have side of larger triangle and height of smaller triangle to get AB

AB = 1-3/4 = 1/4 = 0.25.

IMO option B.
Manager
Manager
User avatar
B
Joined: 24 Aug 2016
Posts: 60
Location: India
WE: Information Technology (Computer Software)
Re: The height of an equilateral triangle is the side of a smaller equilat  [#permalink]

Show Tags

New post 07 Sep 2016, 20:42
If the length of the side of equilateral triangle is a, its height will be \(( \sqrt{3} / 2 ) * a\)

So height of bigger triangle using above formula = \(( \sqrt{3} / 2 ) * 1 = ( \sqrt{3} / 2 )\)

The height of bigger triangle = Length of side of smaller triangle = \(( \sqrt{3} / 2 )\)

Height of Smaller triangle = \(( \sqrt{3} / 2 ) * ( \sqrt{3} / 2 ) = 3/4 = 0.75\)

AB = Length of bigger triangle - Height of slammer triangle = 1 -0.75 = 0.25 (B).
_________________
"If we hit that bullseye, the rest of the dominos will fall like a house of cards. Checkmate."
GMATH Teacher
User avatar
P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: The height of an equilateral triangle is the side of a smaller equilat  [#permalink]

Show Tags

New post 15 Oct 2018, 11:09
Bunuel wrote:
Image
The height of an equilateral triangle is the side of a smaller equilateral triangle, as shown above. If the side of the large equilateral triangle is 1, what is AB?

A. 1 - √3/2
B. 0.25
C. 2 - √3
D. 1/3
E. 1 - √3/4

(The formula below we suggest you memorize. It will be used here twice.)

\({h_{eq}} = {{L\sqrt 3 } \over 2}\,\,\,\,\,\left( * \right)\,\,\,\,\,\,\,\,\left( {{\rm{height}}\,\,{\rm{of}}\,\,{\rm{an}}\,\,{\rm{equilateral}}\,\,{\rm{triangle}}\,\,{\rm{with}}\,\,{\rm{side}}\,\,L} \right)\)

Image

\(? = AB = {L_{\,{\rm{large}}}} - {h_{{\rm{eq}}\,{\rm{small}}}}\,\, = \,\,\,1 - \,\,{?_{{\rm{temporary}}}}\)

\(\Delta \,{\rm{small}}\,\,:\,\,\,\,\,{L_{\,{\rm{small}}}} = {h_{\,{\rm{eq}}\,{\rm{large}}}}\,\,\mathop = \limits^{\left( * \right)} \,\,\,\,{{1 \cdot \sqrt 3 } \over 2}\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{?_{{\rm{temporary}}}} = {h_{{\rm{eq}}\,{\rm{small}}}}\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,{{\sqrt 3 } \over 2} \cdot {{\sqrt 3 } \over 2} = {3 \over 4}\)

\(? = 1 - {3 \over 4} = {1 \over 4}\)

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
GMAT Club Bot
Re: The height of an equilateral triangle is the side of a smaller equilat   [#permalink] 15 Oct 2018, 11:09
Display posts from previous: Sort by

The height of an equilateral triangle is the side of a smaller equilat

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne