Question

The number of rectangles that you can find on a chessboard is equal to?

• A. $144$
• B. $1296$
• C. $256$
• D. None of these

Answer 1

The correct option is B

$1296$

Explanation for correct option

We know that,

The number of horizontal and vertical lines that will form a rectangle is $2$ each.

Total number of rectangles in $n\times n$ chess board is $={}^{n+1}{C}_2\times {}^{n+1}C_2$

Note that the square will also be included in counting of rectangle

The dimension of chess board is $8\times 8$.

So $n=8$

Total number of rectangles in $8\times 8$ chess board is $={}^9{C}_2\times {}^{9}C_2=36\times 36=1296$

Hence, the correct option is $\left(\mathrm{B}\right)$$1296$.