Question

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Q 29. A polygon has 252 diagonals. Determine the number of sides of this polygon.
Ops: A. 027
B. 025
C. 024
D. 23
many days will 21 boys do the same​

Answer 1

if the polygon have 252 diagonals that polygon have it must have 24 sides

Answer 2

Given :   A polygon has 252 diagonals.

To Find : Determine the number of sides of this polygon.

Solution:

Number of diagonals in polygon with sides n

= n(n - 3)/2

n(n - 3)/2  = 252

=> n² - 3n = 504

=> n² - 3n - 504 = 0

=> n²  -  24n  + 21n  - 504  = 0

=> n (n - 24) + 21(n - 24) = 0

=>( n - 24)(n + 21) = 0

=> n = 24  or n = - 21

As number of sides can not be negative

Hence n = 24

So  the number of sides of this polygon is 24

Correct answer is option C) 24

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