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Exploring Number of Squares on the Diagonal of a Rectangle

Touch or click to shade and count the squares at the diagonal. Drag the red point to change the dimensions of the rectangle.

How many squares are there on the diagonal of a 9×5 rectangle?

How many squares are there on the diagonal of a 9×6 rectangle?

How many squares are there on the diagonal of a 12×8 rectangle?

In general, how many squares are there on the diagonal of a m×n rectangle?