A polygon has 44 diagonals. The number of its sides is

Options

A. 11
B. 10
C. 8
D. 7

Answer

To find the number of sides of a polygon that has 44 diagonals, we can use the formula for the number of diagonals in a polygon, which is given by:

\[ D = \frac{n(n - 3)}{2} \]

where \(D\) is the number of diagonals and \(n\) is the number of sides of the polygon.

### Step-by-Step Solution:

1. **Set up the equation using the given number of diagonals**:
We know that the polygon has 44 diagonals, so we can set up the equation:
\[ \frac{n(n - 3)}{2} = 44 \]

2. **Multiply both sides by 2 to eliminate the fraction**:
\[ n(n - 3) = 88 \]

3. **Rearrange the equation**:
\[ n^2 - 3n - 88 = 0 \]

4. **Factor the quadratic equation**:
We need to factor \(n^2 - 3n - 88\). We look for two numbers that multiply to \(-88\) and add to \(-3\). These numbers are \(-11\) and \(8\):
\[ n^2 - 11n + 8n - 88 = 0 \]
This can be factored as:
\[ (n - 11)(n + 8) = 0 \]

5. **Solve for \(n\)**:
Setting each factor to zero gives us:
\[ n - 11 = 0 \quad \text{or} \quad n + 8 = 0 \]
Thus, we find:
\[ n = 11 \quad \text{or} \quad n = -8 \]

6. **Determine the valid solution**:
Since \(n\) represents the number of sides of a polygon, it must be a positive integer. Therefore, we discard \(n = -8\) and keep:
\[ n = 11 \]

### Conclusion:
The number of sides of the polygon is **11**.