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  4. The number of rectangles that can be obtained by joining four of th e twelve vertices of a 12 -sided regular polygon is

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Q. The number of rectangles that can be obtained by joining four of th e twelve vertices of a $12$ -sided regular polygon is

KVPYKVPY 2010

Solution:

We have,
$12$-sided regular polygon the diagonal of rectangle are equal
$\therefore $ Diagonals of rectangle passes through the centre of $12$-sided regular polygon $= 6$
$\therefore $ Number of rectangles $=^{6}C_{2}=\frac{6!}{2!4!}=15$