triangle mno is an equilateral triangle with sides measuring 16\\sqrt{3} units. what is the height of the…

Answer:

B. 24 units

Explanation:

Step1: Divide base in half

In an equilateral triangle, the height bisects the base. So $MR=\frac{16\sqrt{3}}{2}=8\sqrt{3}$ units.

Step2: Apply Pythagorean theorem

In right - triangle $MNR$, let the height $NR = h$, $MN = 16\sqrt{3}$ and $MR=8\sqrt{3}$. By the Pythagorean theorem $h=\sqrt{(16\sqrt{3})^{2}-(8\sqrt{3})^{2}}$.

Step3: Simplify the expression

First, expand the terms: $(16\sqrt{3})^{2}=16^{2}\times3 = 768$ and $(8\sqrt{3})^{2}=8^{2}\times3 = 192$. Then $h=\sqrt{768 - 192}=\sqrt{576}=24$ units.