Question

Attachment below, please help

Answer 1

Answer:

19 ≤  n ≤ 49

Step-by-step explanation:

A polygon with n sides has D diagonals where

D is given by function

D(n) = n(n-3)/2

Find the number of Sides n  

if 152 ≤  D  ≤ 1127

n(n-3)/2 = 152

=> n² - 3n = 304

=> n² - 3n - 304 = 0

=> n² - 19n + 16n - 304 = 0

=> n(n-19) + 16(n-2) = 0

=> (n-19)(n+16) = 0

=> n = 19    ( number of sides can not be -ve)

n(n-3)/2 = 1127

=> n² - 3n = 1127

=> n² - 3n - 2254 = 0

=> n² - 49n + 46n - 2254 = 0

=> n(n-49) + 46(n-49) = 0

=> (n-49)(n+46) = 0

=> n = 49    ( number of sides can not be -ve)

So number of sides

19 ≤  n ≤ 49