NIMCET 2021 — Mathematics PYQ

Solution

1. Formula for the Number of Diagonals

If a polygon has $n$ sides, the number of diagonals is given by the formula:

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

2. Form the Equation

Given that the number of diagonals is $44$, we set up the following equation:

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

3. Solve the Quadratic Equation

Multiply both sides by $2$:

$n(n-3)=88$

$n^2-3n=88$

$n^2-3n-88=0$

4. Factorize the Quadratic

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

$n^2-11n+8n-88=0$

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

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

5. Find the Value of $n$

This gives us two possible values for $n$:

$n-11=0⟹n=11$

$n+8=0⟹n=-8$

Since the number of sides of a polygon cannot be negative, we discard $n=-8$.

Final Answer

The number of sides is:

$11$

The correct option is 2.