Question

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√2 units 16√5 units

Explanation:

Step1: Divide the equilateral triangle

When we draw the altitude of an equilateral triangle, it divides the equilateral triangle into two congruent right - angled triangles. The side of the equilateral triangle (hypotenuse of the right - angled triangle) \(c = 8\) units, and the base of each right - angled triangle \(a=\frac{8}{2}=4\) units. Let the altitude be \(b\).

Step2: Apply the Pythagorean theorem

According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). Substitute \(a = 4\) and \(c = 8\) into the formula:

$$
LATEXBLOCK0
$$

Answer:

\(4\sqrt{3}\) units