Question

The number of rectangles that can be obtained by joining four of the twelve vertices of a $12$ sided regular polygon is

• A. $66$
• B. $30$
• C. $24$
• D. $15$

Answer 1

Answer: (D)

The first vertex can be choosed in $12$ ways and diagonally opposite to it is $1$ vertex. Now for $3rd$ vertex we have $10$ choices and for $4th$ $1.$

However, each rectangle is counted $8$ times.

$\therefore$ No. of ways $=\frac{12\times 1\times 10\times 1}{8}$ $=15$ ways.

Hence, the answer is $15.$