Question

The number of diagonals in a regular polygon of 100 sides is
A. 4950
B. 4850
C. 4750
D. 4650

Answer 1

Hint: The number of diagonals in a regular polygon with n sides = ${}^n{C}_2-n$, using this formula we can directly find the number of diagonals.

We are supposed to find the number of diagonals where the number of sides given to us are 100 therefore, if we apply the formula with n=100, we will obtain the result,
Therefore,
The number of diagonals in a polygon with 100 sides $\Rightarrow {}^{100}{C}_2-100$
Let us solve it, the formula of ${}^n{C}_r={\displaystyle \frac{n!}{r!\left(n-r\right)!}}$,
Therefore the above equation becomes,
 ${}^{100}{C}_2-100={\displaystyle \frac{100!}{2!\left(100-2\right)!}}-100$
${}^{100}{C}_2-100={\displaystyle \frac{100\times 99}{2}}-100$
${}^{100}{C}_2-100={\displaystyle \frac{9900-200}{2}}$
${}^{100}{C}_2-100={\displaystyle \frac{9700}{2}}$
${}^{100}{C}_2-100=4850$
Answer = 4850
Option B is the correct answer in this question.

Note: We started by taking the general formula of calculating the number of diagonals, equated the values and solved the equation to get the final answer.