Question

What is the length of the altitude of the equilateral triangle below?

a. 3
b. 9
c. 3√3
d. 6√3

Answer 1

The length of the altitude of an equilateral triangle can be found using the Pythagorean theorem. In an equilateral triangle, all sides are equal, and the length of the altitude is √3/2 times the length of a side.

Step-by-step explanation:

The length of the altitude of an equilateral triangle can be found using the Pythagorean theorem. In an equilateral triangle, all sides are equal in length. Let's call the length of each side 's'. The altitude of an equilateral triangle divides it into two congruent right triangles. Using the Pythagorean theorem, we can find the length of the altitude:

a² + (s/2)² = s²

Simplifying the equation, we get:

a² + s²/4 = s²

Multiplying both sides by 4:

4a² + s² = 4s²

Subtracting s² from both sides:

4a² = 3s²

Taking the square root of both sides:

2a = √3s

Dividing both sides by 2:

a = √3/2 * s

So, the length of the altitude 'a' of an equilateral triangle is √3/2 * s.