SOLUTION: what is the height of an equilateral triangle if all three of it's sides are 24 inches?

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Question 810413: what is the height of an equilateral triangle if all three of it's sides are 24 inches?
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
a%5E2%2Bb%5E2=c%5E2
sides are (a) and (b)
(c) is longest side
in triangle FGH
where point D is between FH so that it splits it evenly in half at a 90 degree angle
the line FD = line DH
and line GD is perpendicular to line FH
side (a) will represent line FD which is half of Line FH. this making it 12 inches.
side (b) will represent line GD which is the height we are looking for.
side (c) will represent line FG and the size is unchanged at 24 inches
a%5E2%2Bb%5E2=c%5E2
12%5E2%2Bb%5E2=24%5E2
144%2Bb%5E2=576
b%5E2=432
sqrt%28b%5E2%29=sqrt%28432%29
432=2*2*2*2*3*3*3=(4^2)(3^2)3
b=sqrt%283%283%5E2%29%284%5E2%29%29
b=12sqrt%283%29