Question

question 10 of 10
what is the length of the altitude of the equilateral triangle below?

a. $6\sqrt{3}$
b. 2
c. 36
d. 6
e. $2\sqrt{3}$
f. $\sqrt{48}$

Explanation:

Step1: Use Pythagorean theorem

We can use the right triangle formed by the altitude, half the base, and one side of the equilateral triangle. The formula is $a^2 + (2\sqrt{3})^2 = (4\sqrt{3})^2$, where $a$ is the altitude.

Step2: Calculate squared terms

First compute $(2\sqrt{3})^2 = 2^2 \times (\sqrt{3})^2 = 4 \times 3 = 12$, and $(4\sqrt{3})^2 = 4^2 \times (\sqrt{3})^2 = 16 \times 3 = 48$.

Step3: Solve for $a^2$

Rearrange the equation: $a^2 = 48 - 12 = 36$.

Step4: Find $a$

Take the square root: $a = \sqrt{36} = 6$. Also, note $\sqrt{48} = 4\sqrt{3}$ which is not equal to 6, so we confirm $a=6$.

Answer:

D. 6