SOLUTION: if the sides of an equilateral triangle are 10 cm what is the length of the altitude ?

Question 463945: if the sides of an equilateral triangle are 10 cm what is the length of the altitude ?
Found 2 solutions by jorel1380, Theo:
Answer by jorel1380(3719) (Show Source): You can put this solution on YOUR website!
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..
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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).

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