The number of diagonals in a regular polygon of 100 sides is
A. 4950
B. 4850
C. 4750
D. 4650
Last updated date: 21st Mar 2023
•
Total views: 306.3k
•
Views today: 5.86k
Answer
306.3k+ views
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 ${}^n{C_r} = \dfrac{{n!}}{{r!\left( {n - r} \right)!}}$,
Therefore the above equation becomes,
${}^{100}{C_2} - 100 = \dfrac{{100!}}{{2!\left( {100 - 2} \right)!}} - 100$
${}^{100}{C_2} - 100 = \dfrac{{100 \times 99}}{2} - 100$
${}^{100}{C_2} - 100 = \dfrac{{9900 - 200}}{2}$
${}^{100}{C_2} - 100 = \dfrac{{9700}}{2}$
${}^{100}{C_2} - 100 = 4850$
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.
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 ${}^n{C_r} = \dfrac{{n!}}{{r!\left( {n - r} \right)!}}$,
Therefore the above equation becomes,
${}^{100}{C_2} - 100 = \dfrac{{100!}}{{2!\left( {100 - 2} \right)!}} - 100$
${}^{100}{C_2} - 100 = \dfrac{{100 \times 99}}{2} - 100$
${}^{100}{C_2} - 100 = \dfrac{{9900 - 200}}{2}$
${}^{100}{C_2} - 100 = \dfrac{{9700}}{2}$
${}^{100}{C_2} - 100 = 4850$
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.
Recently Updated Pages
Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Write a letter to the Principal of your school to plead class 10 english CBSE
