NIMCET 2011 — Mathematics PYQ

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Question

NIMCET 2011 — Mathematics PYQ

NIMCET | Mathematics | 2011

A polygon has 44 diagonals, the number of its sides is:

Choose the correct answer:

Explanation

1. The Formula:

The number of diagonals $D$ in a polygon with $n$ sides is given by:

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

2. Set up the Equation:

We are given that $D = 44$ . Plugging this into the formula, we get:

44 = \frac{n(n - 3)}{2}

3. Solve for $n$ :

Multiply both sides by 2:

88 = n(n - 3)

88 = n^2 - 3n

Rearrange it into a quadratic equation:

n^2 - 3n - 88 = 0

4. Factorize the Equation:

We need two numbers that multiply to $-88$ and add up to $-3$ . Those numbers are $-11$ and $+8$ .

(n - 11)(n + 8) = 0

This gives us two possible values for $n$ :

$n - 11 = 0 \Rightarrow n = 11$
$n + 8 = 0 \Rightarrow n = -8$

Conclusion:

Since the number of sides of a polygon cannot be negative, we take $n = 11$ .

The correct option is (c) 11.