Question

question 1 of 10
what is the length of the altitude of the equilateral triangle below?
a. 81
b. 9
c. 3√3
d. 9√3
e. 3
f. √108

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle formed by the altitude of the equilateral triangle, if the hypotenuse is $c = 6\sqrt{3}$ and one side is $b = 3\sqrt{3}$, and the altitude is $a$. According to the Pythagorean theorem $a=\sqrt{c^{2}-b^{2}}$.

Step2: Substitute values

Substitute $c = 6\sqrt{3}$ and $b = 3\sqrt{3}$ into the formula:
\[

$$\begin{align*} a&=\sqrt{(6\sqrt{3})^{2}-(3\sqrt{3})^{2}}\\ &=\sqrt{108 - 27}\\ &=\sqrt{81}\\ &=9 \end{align*}$$

\]

Answer:

B. 9