Question

An equilateral triangle has an altitude length of 27 feet. Determined the length of a side of the triangle

Answer 1

Ok equilateral triangle
altitude=27
height=27
if you drwa the height, you see that the equilateral triangle is split up into 2 right trnalges

base=1/2 of one side
hypotonuse=1 side
vertical side=27
represent measure of 1 side as x
base=x/2
hypotonuse=x
vertical side=27

we have a right triangle
use pythagoran theorem
a^2+b^2=c^2
a=x/2
b=27
c=x
so

(x/2)^2+27^2=x^2
(x^2)/4+729=x^2
multiply both sides by 4 to clear fraction
x^2+2916=4x^2
subtract x^2 fromboth sides
2916=3x^2
divide both sides by 3
972=x^2
squuare root both sides
18√3

one side is 18√3 feet or aprox 31.1769 feet