To find the length of the altitude of an equilateral triangle given its side length, we can use the geometric properties of such triangles.
1. Understand the properties of an equilateral triangle:
- An equilateral triangle has all three sides of the same length.
- All interior angles are 60 degrees.
2. Identify the given side length:
- The side length of the equilateral triangle is given as 8 units.
3. Altitude formula for an equilateral triangle:
- The altitude (or height) of an equilateral triangle can be derived from dividing the triangle into two 30-60-90 right triangles, where the altitude forms one leg, half of the base forms the other leg, and the original side is the hypotenuse.
- In a 30-60-90 triangle, the ratios of the sides are [tex]\( 1 : \sqrt{3} : 2 \)[/tex]. The shortest side is half the base of the equilateral triangle, the height is the longer leg, and the hypotenuse is the side of the triangle.
4. Apply the relationship:
- Half the side length is [tex]\( \frac{8}{2} = 4 \)[/tex] units.
- The altitude (height) can then be calculated as follows:
[tex]\[
\text{Altitude} = 4 \sqrt{3}
\][/tex]
5. Final verification:
- Among the given options, [tex]\( 4 \sqrt{3} \)[/tex] units matches our derived value.
Therefore, the length of the altitude of the equilateral triangle is:
[tex]\[
4 \sqrt{3} \text{ units}
\][/tex]
