A polygon has 434 diagonals find the sides of the polygon
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we know the formula ,
number of diagonals = n(n - 3)/2 ,where n is the number of sides .
here given,
number of diagonals = 434
⇒ n(n - 3)/2 = 434
⇒ n² - 3n = 868
⇒ n² - 3n - 868 = 0
⇒ n² - 31n + 28n - 868 = 0
⇒ n( n - 31) + 28(n - 31) = 0
⇒ (n - 31)(n + 28) = 0
n = 31 and - 28 , n ≠ - 28 , number o sides can't be negative.
hence, number of sides = 31
number of diagonals = n(n - 3)/2 ,where n is the number of sides .
here given,
number of diagonals = 434
⇒ n(n - 3)/2 = 434
⇒ n² - 3n = 868
⇒ n² - 3n - 868 = 0
⇒ n² - 31n + 28n - 868 = 0
⇒ n( n - 31) + 28(n - 31) = 0
⇒ (n - 31)(n + 28) = 0
n = 31 and - 28 , n ≠ - 28 , number o sides can't be negative.
hence, number of sides = 31
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