Question 927131
 *[illustration EquilateralTriangleArea.jpg].
The area of an equilateral triangle is 125 sq. cm.
Find its altitude:
I.  Altitude bisects Base
II. 30-60-90 Triangle is formed: Ratio of Sides: 1 : √3 : 2
III. 30-60-90 Triangle formed: sides: s/2, (s/2)√3, s
........
A = {{{(1/2)bh = (1/2)(s)(s*sqrt(3)/2)}}}
A = {{{(1/2)(s)(s*sqrt(3)/2) = 125 cm^2}}}
A = (1/4)s^2 √3 = 125
s ={{{ sqrt( 4*125/sqrt(3))}}} = 17 rounded
h ={{{ 17sqrt(3)/2}}} = 8.5√3 =  14.7 rounded

and...checking
A = {{{(1/2)bh = (1/2)(17)*14.7 }}} = 125 rounded