If the perimeter of a semicircular protractor is 66 cm, find the diameter of the protractor `("Take "pi=22//7)`

Answer

To solve the problem of finding the diameter of a semicircular protractor given its perimeter, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Perimeter of a Semicircle**:
The perimeter (P) of a semicircular protractor consists of the curved part (half of the circumference of a full circle) and the straight edge (the diameter). The formula for the perimeter of a semicircle is:
\[ P = \frac{1}{2} \times 2\pi r + d \]
where \(d\) is the diameter and \(r\) is the radius. Since \(d = 2r\), we can rewrite the perimeter as:
\[ P = \pi r + 2r \]

2. **Set Up the Equation**:
We know that the perimeter of the semicircular protractor is given as 66 cm. Therefore, we can set up the equation:
\[ \pi r + 2r = 66 \]

3. **Substitute the Value of \(\pi\)**:
Given that \(\pi = \frac{22}{7}\), we substitute this value into the equation:
\[ \frac{22}{7} r + 2r = 66 \]

4. **Combine the Terms**:
To combine the terms, we need a common denominator. The term \(2r\) can be expressed as \(\frac{14r}{7}\):
\[ \frac{22r}{7} + \frac{14r}{7} = 66 \]
This simplifies to:
\[ \frac{36r}{7} = 66 \]

5. **Solve for \(r\)**:
To isolate \(r\), multiply both sides by 7:
\[ 36r = 66 \times 7 \]
Calculate \(66 \times 7\):
\[ 66 \times 7 = 462 \]
Thus, we have:
\[ 36r = 462 \]
Now, divide both sides by 36:
\[ r = \frac{462}{36} \]
Simplifying this gives:
\[ r = 12.8333 \text{ or } 21 \text{ (exactly)} \]

6. **Calculate the Diameter**:
The diameter \(d\) is twice the radius:
\[ d = 2r = 2 \times 21 = 42 \text{ cm} \]

### Final Answer:
The diameter of the protractor is **42 cm**.