Question
Find the length of a side of an equilateral triangle with altitude of length 6.
Answers
Reiny
let each side of the triangle be 2x units
then x^2 + 6^2 = (2x^2)
x^2 + 36 = 4x^2
3x^2 = 36
x^2 = 12
x = 2√3
2x = 4√3
or
knowing the ratio of sides of a 30-60-90 triangle
is 1:√3:2
h/2 = 6/√3
√3h=12
h = 12/√3
= 12/√3(√3/√3) = 12√3/3 = 4√3
then x^2 + 6^2 = (2x^2)
x^2 + 36 = 4x^2
3x^2 = 36
x^2 = 12
x = 2√3
2x = 4√3
or
knowing the ratio of sides of a 30-60-90 triangle
is 1:√3:2
h/2 = 6/√3
√3h=12
h = 12/√3
= 12/√3(√3/√3) = 12√3/3 = 4√3