Question

Area of equilateral triangle is 21 under root 3 m^2 find its heigh

Answer 1

area=(3^(1/2)/4) (a)^2
there a = 9 approx value.
now when you drop altitude itr becomes 30-60-90 triangle 
hence altitude opp to 60 therefore
altitude=9*(3)^(1/2)/2
            =4.5*3^1/2

Answer 2

area of equilateral triangle = side^2 (root3/4)

21 root 3 = side^2 (root3/4)

root 3 will cancel

21= side^2/4

21*4 = side^2

84= side^2

root 84 = side 

by pythagoras theorem, 

(root84/2)^2 + (hieght)^2 = (root84)^2

84/4 +(height)^2 = 84

(heigth)^2 = 84-84/4

height^2 = (336-84)/4 

height^2 = 252/4

hiegth^2= 63

height= root 63




i hope this will help you




- by ABHAY