Question

A convex polygon has 44 diagonals. How many side does it have?

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Answer 1

Let the number of sides it have = n.

We know that number of sides of a polygon = n(n - 3)/2

Now,

= > 44 = n(n - 3)/2

= > 88 = n(n - 3)

= > 88 = n^2 - 3n

= > n^2 - 3n - 88 = 0

= > n^2 - 11n + 8n - 88 = 0

= > n(n - 11) + 8(n - 1) = 0

= > (n - 11)(n + 8) = 0

= > n = 11,-8[It should not be negative].

= > n = 11.

Therefore, the convex polygon has 11 sides.

Hope this helps!