Question

what is the length of the altitude of the equilateral triangle below? a. 27 b. 3 c. 6√3 d. 3√3 e. 6 f. 1

Explanation:

Step1: Apply Pythagorean theorem

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

Step2: Substitute values

Substitute $c = 6$ and $b = 3$ into the formula: $a=\sqrt{6^{2}-3^{2}}=\sqrt{36 - 9}=\sqrt{27}=3\sqrt{3}$.

Answer:

D. $3\sqrt{3}$