GMAT Changed on April 16th - Read about the latest changes here

It is currently 23 May 2018, 04:12

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the area of an equilateral triangle that has an altitude of le

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 45266
What is the area of an equilateral triangle that has an altitude of le [#permalink]

Show Tags

New post 26 Apr 2018, 13:31
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

74% (01:40) correct 26% (01:27) wrong based on 37 sessions

HideShow timer Statistics

What is the area of an equilateral triangle that has an altitude of length 24?


(A) \(24 \sqrt{3}\)

(B) \(48 \sqrt{3}\)

(C) \(96 \sqrt{3}\)

(D) \(192 \sqrt{3}\)

(E) \(384 \sqrt{3}\)

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

BSchool Forum Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 2552
Location: India
GPA: 3.12
Premium Member CAT Tests
What is the area of an equilateral triangle that has an altitude of le [#permalink]

Show Tags

New post 26 Apr 2018, 13:58
Bunuel wrote:
What is the area of an equilateral triangle that has an altitude of length 24?


(A) \(24 \sqrt{3}\)

(B) \(48 \sqrt{3}\)

(C) \(96 \sqrt{3}\)

(D) \(192 \sqrt{3}\)

(E) \(384 \sqrt{3}\)



An equilateral triangle of side 2 will have an altitude \(\sqrt{3}\)
(because the altitude of the equilateral triangle will form a 30-60-90 triangle with the base)

Since, the altitude of the equilateral triangle is 24, the side is \(\frac{48}{\sqrt{3}}\)

Formula used: Area(equilateral triangle) = \(\frac{\sqrt{3}}{4} * side^2\)

Therefore, the area of the equilateral triangle for side \(\frac{48}{\sqrt{3}}\) is \(\frac{\sqrt{3}}{4}*48*\frac{48}{3} = 192 \sqrt{3}\) (Option D)
_________________

You've got what it takes, but it will take everything you've got

SC Moderator
avatar
D
Joined: 22 May 2016
Posts: 1668
Premium Member CAT Tests
What is the area of an equilateral triangle that has an altitude of le [#permalink]

Show Tags

New post 26 Apr 2018, 20:05
Bunuel wrote:
What is the area of an equilateral triangle that has an altitude of length 24?


(A) \(24 \sqrt{3}\)

(B) \(48 \sqrt{3}\)

(C) \(96 \sqrt{3}\)

(D) \(192 \sqrt{3}\)

(E) \(384 \sqrt{3}\)

Attachment:
equi4.26.18.png
equi4.26.18.png [ 62.33 KiB | Viewed 388 times ]

• An equilateral triangle's altitude always creates
creates two 30-60-90 triangles
Each vertex = 60°
Vertex B is bisected: two 30° angles
Vertex C = 60°
Point D = two 90° angles

A 30-60-90 triangle has corresponding sides opposite those angles in ratio
\(x : x\sqrt{3} : 2x\)

We need to find \(x\) = \(\frac{1}{2}\) of base

Divide the altitude by \(\sqrt{3}\)
Altitude BD, opposite the 60° angle, corresponds with \(x\sqrt{3}\)
\(x\sqrt{3}=24\)
\(x=\frac{24}{\sqrt{3}}=(
\frac{24}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}})=\frac{24\sqrt{3}}{3}=8\sqrt{3}\)

\(x=8\sqrt{3}=\frac{1}{2}b,\) base*

Area of triangle, \(A=\frac{1}{2}*b*h\)
\(A= (8\sqrt{3}* 24)=192\sqrt{3}\)


Answer D

*No need to find the whole base. Area is divided by 2. But IF you wanted to:
Base = \(2x =(2*8\sqrt{3})=16\sqrt{3}\)
Area, \(A=\frac{b*h}{2}\)
\(A=\frac{16\sqrt{3}*24}{2}=(8\sqrt{3}*24)=192\sqrt{3}\)

_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

Manager
Manager
User avatar
B
Joined: 21 Jan 2015
Posts: 243
Location: India
Concentration: Strategy, Marketing
GMAT 1: 620 Q48 V28
WE: Sales (Consumer Products)
GMAT ToolKit User CAT Tests
What is the area of an equilateral triangle that has an altitude of le [#permalink]

Show Tags

New post 27 Apr 2018, 00:29
Bunuel wrote:
What is the area of an equilateral triangle that has an altitude of length 24?


(A) \(24 \sqrt{3}\)

(B) \(48 \sqrt{3}\)

(C) \(96 \sqrt{3}\)

(D) \(192 \sqrt{3}\)

(E) \(384 \sqrt{3}\)


Ans: E

In equilateral triangle of side a altitude is given by 3^(1/2) (a/2) so we can get the a from here.
and area is 1/2(altitude* side of the triangle) = which here is \(192 \sqrt{3}\)
Ans E
_________________

--------------------------------------------------------------------
The Mind is Everything, What we Think we Become.
Kudos will encourage many others, like me.
Please Give Kudos Image !!
Thanks :-)

Expert Post
Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2611
Location: United States (CA)
Re: What is the area of an equilateral triangle that has an altitude of le [#permalink]

Show Tags

New post 30 Apr 2018, 16:29
Bunuel wrote:
What is the area of an equilateral triangle that has an altitude of length 24?


(A) \(24 \sqrt{3}\)

(B) \(48 \sqrt{3}\)

(C) \(96 \sqrt{3}\)

(D) \(192 \sqrt{3}\)

(E) \(384 \sqrt{3}\)


When we drop an altitude in an equilateral triangle we create two 30-60-90 right triangles in which the altitude is opposite the 60 degree angle; thus, the altitude = side√3/2, thus:

side√3/2 = 24

side = 48/√3

We may recall that the area formula for an equilateral triangle is (side^2 * √3)/4, thus:

area = [(48/√3)^2 * √3]/4

area = 768√3/4 = 192√3

Alternate Solution:

When we drop a perpendicular (altitude) in an equilateral triangle, we create two 30-60-90 triangles, each with a ratio of sides of x : 2x : x√3. The altitude is x√3, and so we have:

x√3 = 24

x = 24/√3

x = (24√3)/3

x = 8√3

We see that 8√3 is the base of one of the 30-60-90 triangles, so the base of the entire equilateral triangle is 16√3.

Using the formula for the area of a triangle: A = 1/2 b x h, we have:

A = (1/2) x 16√3 x 24 = 192√3

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: What is the area of an equilateral triangle that has an altitude of le   [#permalink] 30 Apr 2018, 16:29
Display posts from previous: Sort by

What is the area of an equilateral triangle that has an altitude of le

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.