Question

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

Answer 1

euilateral triangle has all sides the same legnth
the altitude would actually be the height of the triangle
if you were to divide the equilateral triangle into 2 right triangles by spliting the original triangle along the altitude line then you have

triangle with hypotonuse x, base y and height 27
remember that since it i s eqilateral then all sides are same, but since we split the base in 2
hyposonute=1 side
base=1/2side
hypotonuse=x base=1/2x and height =27

we can use the pythagorean theorem and subsitute
a^2+b^2=c^2
a=1/2x
b=27
c=x
(1/2x)^2+27^2=x^2
1/4x^2+729=x^2
multiply both sides by 4
x^2+2916=4x^2
subtract x^2 from both sides
2916=3x^2
divide both sides by 3
972=x^2
square root both sides
$18\sqrt{3}$=x or
31.18 (rounded to the hundreth)

so the legnth of one side is
$18\sqrt{3}$  ft or
31.18 ft