The number of rectangles that chessboard has...
Hint 1: Note that a rectangle on a grid is defined by selecting 2 horizontal grid lines and 2 vertical grid lines.
Hint 2: For an chessboard, there are 9 horizontal lines and 9 vertical lines. Choose 2 of each: .
Hint 3: Compute to find the total rectangles.
Step 1 (Analyze Chessboard Grid): An chessboard consists of 8 rows and 8 columns of squares. To form this grid, there are exactly:
9 horizontal lines
9 vertical lines
Step 2 (Rectangle Construction): A rectangle is uniquely formed by choosing exactly 2 distinct horizontal lines (which define the top and bottom boundaries) and 2 distinct vertical lines (which define the left and right boundaries).
Step 3 (Calculate Combinations): The number of ways to choose these lines is:
Ways to choose 2 horizontal lines from 9:
Ways to choose 2 vertical lines from 9:
Using the product rule, the total number of rectangles is:
Step 4 (Conclusion): The chessboard contains exactly 1296 rectangles.
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