BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Ratio between area of equilateral triangle and Square

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Senior | Next Rank: 100 Posts
Posts: 30
Joined: Sat Aug 30, 2008 12:23 am
Location: Los Angeles CA

Ratio between area of equilateral triangle and Square

by ELYAC Realty » Tue Sep 02, 2008 9:18 pm
Can anyone help with this?

Thanks
Attachments
Ratio of area of Triangle to area of Square.doc
(63.5 KiB) Downloaded 216 times
__________
Brought to you by:
ELYAC Realty Los Angeles Real Estate Agents Specializing in Foreclosure Homes for Sale, Home Loans, and Mortgage Brokers
310.562.0572
Web: www.elyacrealty.com
Blog: https://elyacrealty.wordpress.com/
Services: https://elyacrealty.com/losangelesrealestateagents/
Top
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 124
Joined: Mon May 19, 2008 1:12 pm
Thanked: 3 times

by Nycgrl » Tue Sep 02, 2008 9:51 pm
Area of square = s^2
Area of trainge = 1/2*t* {(sqt3)/4}t

1/2*t* {(sqt3)/4}t = s^2

t^2/S^2 = 4/sqt3

t/s = 2/4rt 3
Top
Junior | Next Rank: 30 Posts
Posts: 15
Joined: Wed Aug 27, 2008 7:57 pm
GMAT Score:760

Two solutions

by reza » Tue Sep 02, 2008 9:54 pm
Plug-in some random numbers : if t = 4 then area of height of triangle will be 2V3 (2 times root 3)
and its area will be 2 * V12 / 2 = V12

Now for the square to have an area of V12,
S * S = 12 ^ (1/4)
then S is root of root 12.

Now the ratio of t/s is :

4 / (12 ^(1/4))
Once found, your weakness is your strength. https://www.gmat760.com
Top
Master | Next Rank: 500 Posts
Posts: 187
Joined: Sat May 24, 2008 5:44 am
Thanked: 6 times
Followed by:1 members

by loki.gmat » Tue Sep 02, 2008 9:56 pm
from data given we have
[3^(1/2)/4]*t^2 = s^2

(t/s)^2 = 4/(3^1/2)

t/s = 2/(3^1/4)

hence IMO D.



Thanks!
Top
User avatar
Senior | Next Rank: 100 Posts
Posts: 30
Joined: Sat Aug 30, 2008 12:23 am
Location: Los Angeles CA

by ELYAC Realty » Tue Sep 02, 2008 10:04 pm
Nycgrl wrote:Area of square = s^2
Area of trainge = 1/2*t* {(sqt3)/4}t

1/2*t* {(sqt3)/4}t = s^2

t^2/S^2 = 4/sqt3

t/s = 2/4rt 3
I was under the impression that the area of an equilateral triangle is: s^2(sqrt3)/4.

And when you use that equation: s^2(sqrt3)/4=s^2(area of square), yo will eventually get sqrt3=4...what am I missing?

[/img]https://www.mathwords.com/a/area_equilat ... iangle.htm
Last edited by ELYAC Realty on Tue Sep 02, 2008 10:12 pm, edited 1 time in total.
__________
Brought to you by:
ELYAC Realty Los Angeles Real Estate Agents Specializing in Foreclosure Homes for Sale, Home Loans, and Mortgage Brokers
310.562.0572
Web: www.elyacrealty.com
Blog: https://elyacrealty.wordpress.com/
Services: https://elyacrealty.com/losangelesrealestateagents/
Top
Master | Next Rank: 500 Posts
Posts: 124
Joined: Mon May 19, 2008 1:12 pm
Thanked: 3 times

by Nycgrl » Tue Sep 02, 2008 10:12 pm
If you look at the question ,side of an equilateral triangle is T and that of square is S.

Question does not say that T= S so we take t and s as different values.

therefore area of traingle is {(srt3)/4}*t

If you still have any doubt let me know
Top
User avatar
Senior | Next Rank: 100 Posts
Posts: 30
Joined: Sat Aug 30, 2008 12:23 am
Location: Los Angeles CA

by ELYAC Realty » Tue Sep 02, 2008 10:24 pm
Can you tell me the algebra of how you went from:

1/2*t* {(sqt3)/4}t = s^2

to

t^2/S^2 = 4/sqt3

to finally

t/s = 2/4rt 3


I still dont know why the area of the triangle isnt: s^2(sqrt3)/4 like it says here: https://www.mathwords.com/a/area_equilat ... iangle.htm

Thanks
__________
Brought to you by:
ELYAC Realty Los Angeles Real Estate Agents Specializing in Foreclosure Homes for Sale, Home Loans, and Mortgage Brokers
310.562.0572
Web: www.elyacrealty.com
Blog: https://elyacrealty.wordpress.com/
Services: https://elyacrealty.com/losangelesrealestateagents/
Top
Junior | Next Rank: 30 Posts
Posts: 29
Joined: Mon Sep 01, 2008 3:24 pm
Thanked: 3 times

by gmat2010 » Wed Sep 03, 2008 5:24 pm
ELYAC Realty wrote:Can you tell me the algebra of how you went from:

1/2*t* {(sqt3)/4}t = s^2

to

t^2/S^2 = 4/sqt3

to finally

t/s = 2/4rt 3


I still dont know why the area of the triangle isnt: s^2(sqrt3)/4 like it says here: https://www.mathwords.com/a/area_equilat ... iangle.htm

Thanks

It's is indeed t^2(sqrt3)/4.

Hence, t^2(sqrt3)/4 = s^2

t^2/s^2 = 4/sqrt3

square root both sides. t/s = 2/(3^(1/4))
Top
Post new topic Post Reply
• Page 1 of 1