The length of a side of an equilateral triangle is 12. Whats the length of the altitude

Question

Equilateral triangle with size length of 12

Answer 1

Hi Idalia,

The altitude of an equilateral triangle forms a 30-60-90 triangle with hypotenuse equal to one side of the original triangle. The altitude also bisects the base. Then the 30-60-90 triangle has long side (hypotenuse) of 12, short side ( half of the base) of 6. Let x = altitude.

Using Pythagoras theorem, 12² = 6² + x²

144 = 36 +x²

108 = x² or x² = (36)(3)

x = √(36)(3) = 6√3