each side of an equilateral triangle measures 12 cm find the height of the triangle

Answer 1

In an equilateral triangle, the height bisects the base and forms a right angle. Therefore, we can use the Pythagorean theorem to find the height.

Let h be the height of the triangle.
Using the Pythagorean theorem: h^2 + (12/2)^2 = 12^2
Simplifying: h^2 + 6^2 = 144
h^2 + 36 = 144
h^2 = 144 - 36
h^2 = 108
Taking the square root of both sides: h = √108
Simplifying: h ≈ 10.39 cm

Therefore, the height of the equilateral triangle is approximately 10.39 cm.