Prove AC^2 = 4 * sqrt(3) / 3 for Equilateral Triangle ABC

[math_phys_bio]

ABC is an equilateral triangle with an area of 1 square cm.
C' is the middle of [AB].

i have to prove that AC^2 = 4 * sqrt(3) / 3

how?

 

[junior_J]

use s = (a+b+c)/2 and area = {s*(s-a)*(s-b)*(s-c)}^2
where a = b = c = x (say)

 

[semc]

i know this aint helping but since the question is also on triangle can i ask how u prove ratio theorem?

 

[junior_J]

ratio theorem ?? as in simillar triangles ??

 

[Plastik]

Write CC' (triangle height) in terms of length AC, then solve using triangle area equation.