Answer :
To determine the altitude of an equilateral triangle with sides of length 8 units, we can use properties of equilateral triangles.
1. Identify the formula for the altitude of an equilateral triangle:
The altitude (height) [tex]\( h \)[/tex] of an equilateral triangle can be calculated using the formula:
[tex]\[ h = \frac{\sqrt{3}}{2} \times \text{side length} \][/tex]
2. Substitute the side length into the formula:
Given that the side length is 8 units, we substitute this value into the formula:
[tex]\[ h = \frac{\sqrt{3}}{2} \times 8 \][/tex]
3. Simplify the expression:
[tex]\[ h = \frac{\sqrt{3} \times 8}{2} \][/tex]
[tex]\[ h = \frac{8\sqrt{3}}{2} \][/tex]
[tex]\[ h = 4\sqrt{3} \][/tex]
Therefore, the altitude of the equilateral triangle with side lengths of 8 units is [tex]\( 4\sqrt{3} \)[/tex] units.
Among the given options:
- [tex]\( 5\sqrt{2} \)[/tex] units
- [tex]\( 4\sqrt{3} \)[/tex] units
- [tex]\( 10\sqrt{2} \)[/tex] units
- [tex]\( 16\sqrt{5} \)[/tex] units
The correct answer is [tex]\( 4\sqrt{3} \)[/tex] units.
1. Identify the formula for the altitude of an equilateral triangle:
The altitude (height) [tex]\( h \)[/tex] of an equilateral triangle can be calculated using the formula:
[tex]\[ h = \frac{\sqrt{3}}{2} \times \text{side length} \][/tex]
2. Substitute the side length into the formula:
Given that the side length is 8 units, we substitute this value into the formula:
[tex]\[ h = \frac{\sqrt{3}}{2} \times 8 \][/tex]
3. Simplify the expression:
[tex]\[ h = \frac{\sqrt{3} \times 8}{2} \][/tex]
[tex]\[ h = \frac{8\sqrt{3}}{2} \][/tex]
[tex]\[ h = 4\sqrt{3} \][/tex]
Therefore, the altitude of the equilateral triangle with side lengths of 8 units is [tex]\( 4\sqrt{3} \)[/tex] units.
Among the given options:
- [tex]\( 5\sqrt{2} \)[/tex] units
- [tex]\( 4\sqrt{3} \)[/tex] units
- [tex]\( 10\sqrt{2} \)[/tex] units
- [tex]\( 16\sqrt{5} \)[/tex] units
The correct answer is [tex]\( 4\sqrt{3} \)[/tex] units.
