Last visit was: 10 Apr 2025, 21:56 It is currently 10 Apr 2025, 21:56
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

GRE Prep 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 GRE 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
PREVIOUS TOPIC
NEXT TOPIC

The area of an equilateral triangle with a side length of 4

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 31527
Own Kudos [?]: 37728 [0]
Given Kudos: 26237
Send PM
The area of an equilateral triangle with a side length of 4 [#permalink] New post   01 Sep 2020, 03:44
Expert Reply
00:00

Question Stats:

55% (00:48) correct 44% (00:53) wrong based on 29 sessions

Hide Show timer Statistics

Quantity A
Quantity B
The area of an equilateral triangle with a side length of 4
The area of an isosceles right triangle with a hypotenuse of 4\( \sqrt{2}\)



A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.


KUDOS for the right solution and explanation
ShowHide Answer
Official Answer
B
User avatar
Farina
Senior Manager
Senior Manager
Joined: 10 Feb 2020
Posts: 496
Own Kudos [?]: 357 [0]
Given Kudos: 299
Send PM
Re: The area of an equilateral triangle with a side length of 4 [#permalink] New post   03 Sep 2020, 01:24
1
Area of Equilateral Triangle:
\(S^2\sqrt{3}\)/4

Given side = 4
So A = 4\(\sqrt{3}\)

Area of Isosceles Right Triangle:
A = \(\frac{1}{2}\) L * B
We know the ratio of sides:
x:x:x\(\sqrt{2}\) = L:B:H

Given, H = 4\(\sqrt{2}\)
so x\(\sqrt{2}\) = 4\(\sqrt{2}\)
x = 4
and
A = \(\frac{1}{2}\) 4 * 4
A = 8

So Quantity B is greater
avatar
Olasunbo
Manager
Manager
Joined: 08 Aug 2020
Posts: 92
Own Kudos [?]: 108 [0]
Given Kudos: 0
Send PM
Re: The area of an equilateral triangle with a side length of 4 [#permalink] New post   03 Sep 2020, 04:49
1
An Equilateral triangle can be further broken into 30:60:90 triangle, then the hypotenuse will be 4, shortest side will be 2 while the medium side(height of the triangle) will be 2√3 (following the law of 30:60:90 triangle x:x√3:2x)
The the area will be 1/2*4*2√3= 4√3...

An isocles right angle triangle means 2 sided will be equal (this implies that apart from the 90 degree angle the other angles will be 45 each)
Then 45:45:90 triangle will equal x:x:x√2
Since the hypotenuse is 4 which denote x
Then the other 2 sides will be 4 each
Area = 1/2*4*4=8

Hence answer equal B

Posted from my mobile device Image
User avatar
Farina
Senior Manager
Senior Manager
Joined: 10 Feb 2020
Posts: 496
Own Kudos [?]: 357 [0]
Given Kudos: 299
Send PM
Re: The area of an equilateral triangle with a side length of 4 [#permalink] New post   03 Sep 2020, 22:51
Olasunbo wrote:
An Equilateral triangle can be further broken into 30:60:90 triangle, then the hypotenuse will be 4, shortest side will be 2 while the medium side(height of the triangle) will be 2√3 (following the law of 30:60:90 triangle x:x√3:2x)
The the area will be 1/2*4*2√3= 4√3...


Hi, can you please explain how did you get 2\(\sqrt{3}\)as one of the sides of equilateral triangle? if x = 4 then why x\(\sqrt{3}\) is not equal to 4\(\sqrt{3}\)?
avatar
Olasunbo
Manager
Manager
Joined: 08 Aug 2020
Posts: 92
Own Kudos [?]: 108 [0]
Given Kudos: 0
Send PM
Re: The area of an equilateral triangle with a side length of 4 [#permalink] New post   03 Sep 2020, 23:39
1
Farina wrote:
Olasunbo wrote:
An Equilateral triangle can be further broken into 30:60:90 triangle, then the hypotenuse will be 4, shortest side will be 2 while the medium side(height of the triangle) will be 2√3 (following the law of 30:60:90 triangle x:x√3:2x)
The the area will be 1/2*4*2√3= 4√3...


Hi, can you please explain how did you get 2\(\sqrt{3}\)as one of the sides of equilateral triangle? if x = 4 then why x\(\sqrt{3}\) is not equal to 4\(\sqrt{3}\)?

Remember the triangle is broken into 2 equal part(30:60:90) hence the base is divided into 2 equal part

Posted from my mobile device Image
Prep Club for GRE Bot
gmatclubot
Re: The area of an equilateral triangle with a side length of 4 [#permalink]
03 Sep 2020, 23:39
Moderators:
adewale223
GRE Instructor
108 posts
bronaugust
GRE Forum Moderator
37 posts
BrushMyQuant
Moderator
1131 posts
VibhuAnurag
GRE Instructor
234 posts

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

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact