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

Redeem

Triangles.

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 62
Joined: Mon Aug 02, 2010 3:25 pm
Thanked: 3 times

Triangles.

by Taniuca » Sat Oct 08, 2011 7:44 am
i do not know in what part of the algebra i'm failing.

If P is the perimeter od an equilateral triangle, which of the followinf is the hight?
A) p/3
B) P* Sqr 3
C) p/4
D) p* sqr 3/6
E) p/6

Correct answer is D, if I pkug numbers i get the answer but when i do it with algebra I get b.
I wou,d like to know how to solve the problem with algebra. Tks!

I used p/3 as each one of the values for the sides.
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 349
Joined: Wed Sep 28, 2011 3:38 pm
Location: Austin, TX
Thanked: 236 times
Followed by:54 members
GMAT Score:770

by GmatMathPro » Sat Oct 08, 2011 7:54 am
1. Label each side of the triangle p/3.

2. Draw an altitude from the top vertex to the opposite side and label it 'h'. This will split the bottom side in half into lengths of p/6 and p/6.

3. Now you can either use A)30-60-90 triangle ratios or B)pythagorean theorem.

A) p/3 is across from the 30 degree angle and h is across from 60. The 30-60-90 triangle ratios say that the side across from the 60 degree angle is always √3 times the side opposite the 30 degree angle. Hence, h=(p/6)√3 or p√3/6.

B) (p/6)^2+h^2=(p/3)^2

p^2/36+h^2=p^2/9

h^2=p^2/9-p^2/36

h^2=4p^2/36-p^2/36

h^2=3p^2/36

h^2=p^2/12

h=√(p^2/12)

h=p/√12

h=(p√12)/12

h=2p√3/12

h=p√3/6
Pete Ackley
GMAT Math Pro
Free Online Tutoring Trial
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Sat Oct 08, 2011 7:58 am
Taniuca wrote:i do not know in what part of the algebra i'm failing.

If P is the perimeter od an equilateral triangle, which of the followinf is the hight?
A) p/3
B) P* Sqr 3
C) p/4
D) p* sqr 3/6
E) p/6

Correct answer is D, if I pkug numbers i get the answer but when i do it with algebra I get b.
I wou,d like to know how to solve the problem with algebra. Tks!

I used p/3 as each one of the values for the sides.
Let s = side of equilateral triangle.
P = 3s implies s = P/3
Let h = height of equilateral triangle.
Then by Pythagoras Theorem, s² = h² + s²/4 implies h² = s² - s²/4 = 3s²/4
h = s√3/2 = P√3/6

The correct answer is D.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
Senior | Next Rank: 100 Posts
Posts: 99
Joined: Sun Mar 13, 2011 12:42 pm

by factor26 » Sat Oct 08, 2011 10:19 pm
can someone solve this question by plugging in #'s?

this is where i got to

- i picked a # for p (perimeter); p = 18

therefore ... each side is equal to 6

cut the equilaterial triangle in half and use the pythagorean theorm ; a^2 + b^2 = c^2

3^2 + b^2 = 6^2
9 + b^2 = 36
b^2 = 27
b=sqrt 9 x sqrt 3

b = 3xsqrt3

but now i'm lost .... can someone use my #'s and apply them to the answer choices to find the correct answer? thanks!
Top
User avatar
GMAT Instructor
Posts: 349
Joined: Wed Sep 28, 2011 3:38 pm
Location: Austin, TX
Thanked: 236 times
Followed by:54 members
GMAT Score:770

by GmatMathPro » Sun Oct 09, 2011 6:45 am
Taniuca wrote: A) p/3
B) P* Sqr 3
C) p/4
D) p* sqr 3/6
E) p/6
You chose p=18 and got height h=3√3.

A)p/3=18/3=6 Nope.
B)p√3=18√3 Nope.
C)p/4=18/4 Nope.
D)p√3/6=18√3/6=3√3 SUCCESS!
E)p/6=18/6=3 Nope.
Pete Ackley
GMAT Math Pro
Free Online Tutoring Trial
Top
Master | Next Rank: 500 Posts
Posts: 401
Joined: Tue May 24, 2011 1:14 am
Thanked: 37 times
Followed by:5 members

by MBA.Aspirant » Sun Oct 09, 2011 8:30 am
there's a formula directly for the height of an equilateral triangle, much like the area.

Height of equilateral triangle = s√3/2

Area of equilateral triangle = (s^2√3)/4


so here side = P/3, height = P/3 √3/2 = P√3/6
Top
Senior | Next Rank: 100 Posts
Posts: 99
Joined: Sun Mar 13, 2011 12:42 pm

by factor26 » Sun Oct 09, 2011 10:44 am
It should also be mentioned we can use our P = 18 and height = 3*sqrt3 (appx. 5.1) to find the answer.

we need the answer to come out to 3*sqrt3; which is appx. 5.1

plug in p=18 into our answer choices

a - p/3 ---18/3 = 6 no good

b - p * sqrt 3 --- lets come back to this

c - p/4 --- 18/4 = 4.5 --- no good

d - p * sqrt 3 / 6 --- lets come back to this

e - p/6 ---18/6 = 3 --- no good

D. 18 / 1 * 1.7 / 6
= 3 * 1.7 --- 5.4 --- the answer we were looking for!

GMAT MATH PRO THANKS FOR YOUR HELP! I GOT CONFUSED WITH WHAT ANSWER CHOICE D LOOKED LIKE ... I THOUGHT IT WAS 18 * SQRT(3/6) ... CHEERS FELLAS!! THANK YOU ALL!!
Top
Post new topic Post Reply
• Page 1 of 1