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Combination Based on Geometry

A polygon has...

Question

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

A

8

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B

9

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C

10

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D

11

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Solution

The correct option is D 11
If a polygon has n sides then number of diagonals $\frac{n (n - 3}{2} = 44 [R e f .6 .2 .7]$
n(n–3) = 88 = 11.8 = 11(11 – 3)
$∴ n = 11$ .

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