The circumference of a circle is equal to the perimeter of an equilateral triangle. If the radius of the circle is 7 cm what is the length of the equilateral triangle ?

Options

A. `(22)/(3)cm`
B. `(44)/(3)cm`
C. 44 cm
D. 22 cm

Answer

To solve the problem, we need to find the length of one side of an equilateral triangle given that the circumference of a circle is equal to the perimeter of that triangle, and the radius of the circle is 7 cm.

### Step-by-Step Solution:

1. **Calculate the Circumference of the Circle:**
The formula for the circumference \( C \) of a circle is given by:
\[ C = 2 \pi r \]
Here, the radius \( r \) is 7 cm. Substituting the value of \( r \):
\[ C = 2 \times \frac{22}{7} \times 7 \]
Simplifying this:
\[ C = 2 \times 22 = 44 \text{ cm} \]

2. **Set the Circumference Equal to the Perimeter of the Equilateral Triangle:**
The perimeter \( P \) of an equilateral triangle is given by:
\[ P = 3 \times \text{side} \]
Since the circumference of the circle is equal to the perimeter of the triangle:
\[ 3 \times \text{side} = 44 \text{ cm} \]

3. **Solve for the Length of One Side of the Equilateral Triangle:**
To find the length of one side, we can rearrange the equation:
\[ \text{side} = \frac{44}{3} \text{ cm} \]

### Final Answer:
The length of one side of the equilateral triangle is:
\[ \frac{44}{3} \text{ cm} \]

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