NIMCET 2012 — Mathematics PYQ

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Question

NIMCET 2012 — Mathematics PYQ

NIMCET | Mathematics | 2012

In which of the following regular polygons, the number of diagonals is equal to the number of sides?

Choose the correct answer:

Explanation

Step 1: Formula for the number of diagonals

For a polygon with $n$ sides, the number of diagonals is given by the formula:

\text{Number of diagonals} = \frac{n(n - 3)}{2}

Step 2: Set the condition

The problem states that the number of diagonals is equal to the number of sides ( $n$ ). So, we set up the following equation:

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

Step 3: Solve for $n$

Assuming $n \neq 0$ (as a polygon must have sides):

n(n - 3) = 2n

n - 3 = 2

n = 5

Step 4: Identify the polygon

A polygon with $5$ sides is called a Pentagon.