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The sides of an equilateral triangle are 8 units long. What is the length of the altitude of the triangle?

A. [tex]\(5 \sqrt{2}\)[/tex] units
B. [tex]\(4 \sqrt{3}\)[/tex] units
C. [tex]\(10 \sqrt{2}\)[/tex] units
D. [tex]\(16 \sqrt{5}\)[/tex] units

Sagot :

GinnyAnswer
To find the length of the altitude of an equilateral triangle with a side length of 8 units, we use the following steps:

1. Recall the formula for the altitude [tex]\( h \)[/tex] of an equilateral triangle with side length [tex]\( a \)[/tex]:
[tex]\[ h = \frac{a \sqrt{3}}{2} \][/tex]

2. Substitute the given side length [tex]\( a = 8 \)[/tex] units into the formula:
[tex]\[ h = \frac{8 \sqrt{3}}{2} \][/tex]

3. Simplify the expression:
[tex]\[ h = 4 \sqrt{3} \][/tex]

Therefore, the altitude of the equilateral triangle with a side length of 8 units is [tex]\( 4 \sqrt{3} \)[/tex] units.

So, the correct answer is:
[tex]\[ 4 \sqrt{3} \text{ units} \][/tex]
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