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Triangle MNO is an equilateral triangle with sides measuring [tex][tex]$16 \sqrt{3}$[/tex][/tex] units.

What is the height of the triangle?

A. 12 units
B. 24 units
C. 36 units
D. 72 units

Sagot :

GinnyAnswer
To determine the height of an equilateral triangle when the side lengths are given, we can use the relationship between the side length and the height of an equilateral triangle.

Let's denote the side length of the equilateral triangle as [tex]\( s \)[/tex]. In an equilateral triangle, the height [tex]\( h \)[/tex] can be found using the formula:
[tex]\[ h = \frac{\sqrt{3}}{2} \times s \][/tex]

Given that the side length [tex]\( s \)[/tex] is [tex]\( 16 \sqrt{3} \)[/tex] units, we need to substitute this value into the formula to find the height.

[tex]\[ h = \frac{\sqrt{3}}{2} \times 16\sqrt{3} \][/tex]

Now, simplify the expression step by step:

1. First, multiply the constants:
[tex]\[ \frac{\sqrt{3}}{2} \times 16 = \frac{16 \sqrt{3}}{2} = 8 \sqrt{3} \][/tex]

2. Now multiply [tex]\( 8 \sqrt{3} \)[/tex] by [tex]\( \sqrt{3} \)[/tex]:
[tex]\[ 8 \sqrt{3} \times \sqrt{3} = 8 \times (\sqrt{3} \times \sqrt{3}) = 8 \times 3 = 24 \][/tex]

So, the height of the equilateral triangle MNO is:
[tex]\[ 24 \text{ units} \][/tex]

Thus, the correct option is:
[tex]\[ 24 \text{ units} \][/tex]
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