Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Explore thousands of questions and answers from knowledgeable experts in various fields on our Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
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 hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.