Question
Mon January 24, 2011 By: Mahesh Padmanabh

How many rectangles are there in a CHESS BOARD??

Expert Reply
Thu January 27, 2011
Dear Student,
 
Observe that on an n-by-n chessboard, there are n + 1 vertical lines and n + 1 horizontal lines. These lines form the grid for the chessboard.

When we form a rectangle, we choose two of the vertical lines and two of the horizontal lines. (Notice that our choice of lines determines the size of the rectangle formed.)

So, the number of rectangles is given by the formula:
 


Hence, For a 8 by 8 chessboard, the number of rectangles is = 
 
Regards Topperlearning.
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