Question

Find the altitude of an equilateral triangle of side 10 cm.

Answer 1

If all sides are equal, then 1/2 of one side is 5 cm. 
10^2-5^2=a^2

100-25=a^2
a^2=75
a=√75=√3√25=5√3.

There is an alternate method more simpler too:

the sides of an equilateral triangle are 10 cm.
what is the length of the altitude?
drop an altitude from one of the angles to the opposite side.
that altitude will be perpendicular to the opposite side and will cut the opposite side exactly in half to form 2 right triangles.
each of those right triangles will have a hypotenuse of 10 cm and a base let of 5 cm.
use the pythagorean formula to find the other leg.
that leg will be the altitude.

call that leg x.
you get x^2 + 5^2 = 10^2 which becomes x^2 + 25 = 100 which becomes x^2 = 75 which becomes x = sqrt(75).
that's the length of your altitude.
you can simplify that to make it 5*sqrt(3). 

Hope This helps :)

Answer 2

we know that the altitude in an equilateral triangle is the median
so in smaller ∆ formed
by using Pythagoras theorem we will see dat
10^2= altitude^2+5^2
100= a^2+25
75= a^2
√75=a