If a polygon of n sides has 275 diagonals,the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) 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 $275$,we have

Vedclass · Accepted Answer

$25$

Vedclass · Answer

(A) 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 $275$,we have:$\frac{n(n-3)}{2} = 275$$n(n-3) = 550$$n^2 - 3n - 550 = 0$Solving the quadratic equation using the quadratic formula $n = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$:$n = \frac{3 \pm \sqrt{(-3)^2 - 4(1)(-550)}}{2(1)}$$n = \frac{3 \pm \sqrt{9 + 2200}}{2}$$n = \frac{3 \pm \sqrt{2209}}{2}$$n = \frac{3 \pm 47}{2}$Since $n$ must be positive,$n = \frac{3 + 47}{2} = \frac{50}{2} = 25$.Thus,the number of sides $n$ is $25$.

If a polygon of $n$ sides has $275$ diagonals,then $n$ is

Similar Questions

Out of $n$ points in a plane,$p$ points are collinear. (No three of the remaining points are collinear). The number of lines that can be drawn passing through these points is:

If three distinct vertices are chosen at random from the vertices of a cube,then the probability that they form the vertices of an equilateral triangle is:

$A$ polygon has $44$ diagonals. Then the number of sides of the polygon is:

Out of $18$ points in a plane,no three are in the same straight line except five points which are collinear. The number of $(i)$ straight lines and $(ii)$ triangles which can be formed by joining them is:

The number of diagonals that can be drawn in an octagon is

Vedclass Test Series

Exam Paper Generator

Online Exam Module