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Byju's Answer
Standard XII
Mathematics
Combination
In a polygon ...
Question
In a polygon the number of diagonals is 54. The number of sides of the polygon is
A
10
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B
12
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C
9
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D
none of these
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Solution
The correct option is
B
12
We know,
Number of diagonal in a polygon having
n
side is
=
n
(
n
−
3
)
2
=
54
(given)
⇒
n
(
n
−
3
)
=
54
×
2
=
108
=
12
⋅
9
⇒
n
=
12
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