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

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!

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.

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

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!!