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A polygon has 44 diagonals. Find the number of its side?

Last updated date: 15th Jul 2024
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Hint: It is given that the polygon has 44 diagonal. So, apply the formula of diagonals of a polygon to obtain a quadratic equation of n. Solve the quadratic equation and then obtain the value of n by neglecting the negative value as the number of sides cannot be negative.

Formula used:
A polygon with n sides have \[\dfrac{{n(n - 3)}}{2}\] diagonals.

Complete step by step solution:
It is given that the polygon has 44 diagonals.
\[\dfrac{{n(n - 3)}}{2} = 44\]
\[{n^2} - 3n - 88 = 0\]
\[{n^2} - 11n + 8n - 88 = 0\]
\[n(n - 11) + 8(n - 11) = 0\]
\[(n + 8)(n - 11) = 0\]
\[n = - 8\] or \[n = 11\]
But number of sides of a polygon cannot be negative, therefore n=11.

The correct option is C.

Additional information: A polygon is a geometric object with two dimensions and a finite number of sides. A polygon's sides are made up of segments of straight lines that are joined end to end. As a result, a polygon's line segments are called its sides or edges. Vertex or corners correspond to the intersection of two line segments, where an angle is created. Having three sides makes a triangle which is a polygon. A circle is a plane figure as well, but it isn't regarded as a polygon because it's curved and without sides and angles. So, while all polygons are two-dimensional shapes, not all two-dimensional figures are polygons.

Note: Sometime students get confused and substitute 44 for n in the expression \[\dfrac{{n(n - 3)}}{2}\] and calculate to obtain the number of sides but this expression is for diagonal so we have to equate the expression \[\dfrac{{n(n - 3)}}{2}\] to 44 and solve to obtain n, where n is the number of sides.