Question

finding the length of an altitude
the sides of an equilateral triangle are 8 units long.
what is the length of the altitude of the triangle?
5√2 units
4√3 units
10√5 units
16√5 units

Explanation:

Step1: Recall the formula for the altitude of an equilateral triangle

The formula for the altitude \( h \) of an equilateral triangle with side length \( a \) is \( h=\frac{\sqrt{3}}{2}a \).

Step2: Substitute the given side - length into the formula

Given \( a = 8 \) units. Substitute \( a=8 \) into \( h=\frac{\sqrt{3}}{2}a \), we get \( h=\frac{\sqrt{3}}{2}\times8 \).

Step3: Simplify the expression

\( h = 4\sqrt{3} \) units.

Answer:

\(4\sqrt{3}\) units