Statement-1: If a polygon has 45 diagonals,th | vedclass

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(D) The number of diagonals in a polygon with $n$ sides is given by the formula $\frac{n(n-3)}{2}$.Given that the number of diagonals is $45$,we have

Vedclass · Accepted Answer

Statement-$1$ is false,Statement-$2$ is true.

Vedclass · Answer

(D) The number of diagonals in a polygon with $n$ sides is given by the formula $\frac{n(n-3)}{2}$.Given that the number of diagonals is $45$,we have $\frac{n(n-3)}{2} = 45$.$n(n-3) = 90$.$n^2 - 3n - 90 = 0$.$(n-12)(n+9) = 0$.Since $n$ must be positive,$n = 12$.Thus,Statement-$1$ is false because the number of sides is $12$,not $10$.Statement-$2$ states that out of $n$ points,$2$ points can be selected in $^nC_2$ ways,which is a standard combinatorial result.Therefore,Statement-$1$ is false and Statement-$2$ is true.

Statement-$1$: If a polygon has $45$ diagonals,then the number of sides is $10$. Statement-$2$: Out of $n$ non-collinear points,$2$ points can be selected in $^nC_2$ ways.

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