Question

A polygon has 44 diagonals. Then the number of sides of the polygon are 
 

• A. 11
• B. 12
• C. 10
• D. 13

Hint:

Instead of setting up and factoring the full quadratic expression, plug the given multiple-choice numbers directly into the factored template $n(n-3) = 88$. Testing option (A) gives $11 \times (11-3) = 11 \times 8 = 88$, validating the solution instantly!
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Answer 1

The Correct Option is A

Step 1: Understanding the Question:
A polygon has exactly 44 diagonals. Determine how many sides (n) it possesses.

Step 2: Key Formula or Approach:
From n vertices, total line segments = ⁿC₂ = n(n-1)/2. Subtracting the n boundary edges leaves the diagonals: Number of diagonals = n(n-3)/2.

Step 3: Detailed Explanation:
Set the formula equal to 44: n(n-3)/2 = 44 → n(n-3) = 88 → n² - 3n - 88 = 0. Factorizing: (n - 11)(n + 8) = 0, giving n = 11 or n = -8. Since a polygon cannot have a negative number of sides, n = 11.

Step 4: Final Answer:
The polygon has 11 sides, option (A).