To find the height of an equilateral triangle with side length [tex]\( a \)[/tex], we can use the formula for the height of an equilateral triangle:
[tex]\[ h = \frac{\sqrt{3}}{2} \times a \][/tex]
Given that the side length [tex]\( a \)[/tex] is [tex]\( 16 \sqrt{3} \)[/tex] units, we can substitute this value into the formula:
[tex]\[ h = \frac{\sqrt{3}}{2} \times 16 \sqrt{3} \][/tex]
Next, we need to simplify the expression:
First, calculate the product of [tex]\(\sqrt{3} \times \sqrt{3}\)[/tex]:
[tex]\[ \sqrt{3} \times \sqrt{3} = 3 \][/tex]
Now, multiply this result by 16:
[tex]\[ 3 \times 16 = 48 \][/tex]
Finally, take half of this value, since we are multiplying by [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[ \frac{48}{2} = 24 \][/tex]
So, the height of the equilateral triangle MNO is:
[tex]\[ 24 \, \text{units} \][/tex]
Thus, the correct answer is:
[tex]\[ 24 \, \text{units} \][/tex]
