Question

A polygon has 1274 diagonals.No of sides is

Answer 1

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We know that a regular with n sides ,

• Total diagonals = n(n-3)/2

So Let the Number of sides of this polygon are n.

Then,

➛n (n-3)/2 = 1274

➛n² - 3n = 1274 ° 2

➛n² - 3n - 2548 = 0

➛n² - 52x ± 49x - 2548 = 0

➛n (n-52) ± 49 (x - 52) = 0

❍n = 52 or (-49) Since, value of sides cant be negative.

❍Therefore The Number of sides of this Polygon are 52.