Question

If all possible diagonals formed are 740 then find the number of sides​

Answer 1

40 sides

Explanation:

The number os sides can be calculated using

`(n(n-3))/(2)` = d ( n is number of sides and d number of diagonals )

Here d = 740 , then

`(n(n-3))/(2)` = 740 ( multiply both sides by 2 )

n(n - 3) = 1480

n² - 3n = 1480 ( subtract 1480 from both sides )

n² - 3n - 1480 = 0 ← in standard form

(n - 40)(n + 37) = 0 ← in factored form

Equate each factor to zero and solve for n

n - 40 = 0 ⇒ n = 40

n + 37 = 0 ⇒ n = - 37

A polygon cannot have a negative number of sides.

Then number of sides is 40