The sides of an equilateral triangle are 8 units long.

What is the length of the altitude of the triangle?

A. \(\frac{5}{2}\) units

B. \(\frac{4}{3}\) units

C. \(\frac{10}{2}\) units

D. [tex]\(\frac{16}{5}\)[/tex] units



Answer :

Sure! Let's solve the problem step-by-step to find the length of the altitude of an equilateral triangle with side lengths of 8 units.

### Step 1: Understanding the equilateral triangle
An equilateral triangle is a triangle in which all three sides are equal in length, and all three angles are equal to 60 degrees.

### Step 2: Finding the altitude
The altitude of an equilateral triangle can be found using a known geometric formula.

### Step 3: Formula for the altitude
The altitude (\(h\)) of an equilateral triangle with side length (\(a\)) is given by:
[tex]\[ h = \frac{\sqrt{3}}{2} \times a \][/tex]

### Step 4: Plug in the given side length
Given the side length (\(a\)) is 8 units:
[tex]\[ h = \frac{\sqrt{3}}{2} \times 8 \][/tex]

### Step 5: Simplifying the expression
[tex]\[ h = 4 \sqrt{3} \][/tex]

### Step 6: Calculating the numerical value (Given answer)
The numerical value of \(4 \sqrt{3}\) is approximately:
[tex]\[ h \approx 6.928203230275509 \][/tex]

Therefore, the length of the altitude of the equilateral triangle is approximately 6.928 units.