https://file.aiquickdraw.com/mathbot/file/1725977837493libmc3bz.jpg

The text in the image you uploaded is written in Bengali and contains a mathematical problem. Here is its translated version:

---

"If the radius of a circle is the distance from its center to a vertex of an equilateral triangle inscribed in the circle, then what is the side length of the triangle? The radius of the circle is 2 meters."

---

### Step-by-Step Explanation:

1. **Known Information:**
   - The circle has a radius (\(R\)) of 2 meters.
   - An equilateral triangle is inscribed in the circle. The vertices of the triangle touch the circle, meaning the radius of the circle is the distance from the center of the circle to one of the vertices of the triangle.

2. **Formula for the relationship between the side length (\(s\)) of an equilateral triangle and the radius (\(R\)) of the circumscribed circle:**
   \[
   R = \frac{s}{\sqrt{3}}
   \]

3. **Solving for \(s\) (side length of the triangle):**
   \[
   s = R \times \sqrt{3}
   \]
   Given that \(R = 2\) meters:
   \[
   s = 2 \times \sqrt{3} \approx 2 \times 1.732 = 3.464 \, \text{meters}
   \]

### Final Answer:
The side length of the equilateral triangle is approximately **3.464 meters**.

---

Would you like further details on this solution, or do you have any other questions?

Here are 5 related questions to expand your understanding:
1. How is the formula \( R = \frac{s}{\sqrt{3}} \) derived?
2. What is the significance of the circumradius in an equilateral triangle?
3. How would the solution change if the triangle were not equilateral?
4. Can the same approach be used for a square or another polygon inscribed in a circle?
5. How do you calculate the area of an equilateral triangle if the side length is known?

**Tip:** Always remember that the radius of a circumscribed circle for regular polygons has a specific relationship with the side length, which can be derived geometrically.

If the radius of a circle is the distance from its center to a vertex of an equilateral triangle inscribed in the circle, what is the side length of the triangle? The radius of the circle is 2 meters.

Learn how to calculate the side length of an equilateral triangle inscribed in a circle with a radius of 2 meters. This geometry problem involves the formula connecting the side length and the radius of the circumscribed circle. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation