Question

Q 22 A polygon has 1274 diagonals. Determine the number of sides of this polygoon​

Answer 1

Given :- A polygon has 1274 diagonals .

To Find :- number of sides of this polygon .

Answer :-

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)(n + 49) = 0

→ n = 52 or (-49) . since value of sides cant be in negative .

therefore, the number of sides of this polygon are 52.