Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Get detailed and accurate answers to your questions from a community of experts on our comprehensive Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
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.
We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.