Question

what is the height of an equilateral triangle with sides that are 10 cm long?

Answer 1

area of equilateral triangle by herons formula is √3/4xa^2

here a is 10cm

so

√3/4x10^2
=√(3)/4x100
=√(3)x25
=25√(3)


area is 1/2basexheight

so a=1/2x10xh

25√(3)=5h

h=25√(3)/5

so height is 5√(3)

Answer 2

We know that area of an equilateral triangle is √3/4*a², where a=side of the triangle. We are given a=10 cm so,
area=√3/4*100=25√3
Now, we have the area of the triangle, so let's find out the height by the formula-
area=1/2*base*height (as it is an equilateral triangle, base=10cm)
25√3=1/2*10*h
25√3=5*h
(25√3)/5=h
h=5√3cm

Hope this helps..!!