Question

What is the length of an equilateral triangle whose altitude has a length of 21

Answer 1

Let each side be 2x
then we would have a right-angled triangle with sides, x, 21, and 2x so that
x^2 + 21^2 = (2x)^2
3x^2= 441
x^2 = 147
x = √147 = 7√3

so each side of the equilateral triangle is 14√3


or using trig

let each side be s
then 21/s =sin60°
s = 21/sin60° = 21/(√/2) = 42/√3
= 14√3 after rationalizing the denominator, same asnwer as above.