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

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