A 24-foot by 72-foot rectangular dance floor is completely tiled with 1-foot by 1-foot square tiles. Two opposite corners of the dance floor are connected be a diagonal. This diagonal passes through the interior of exactly how many tiles?
A 24-foot by 72-foot rectangular dance floor is completely tiled with 1-foot by 1-foot square tiles. Two opposite corners of the dance floor are connected be a diagonal. This diagonal passes through the interior of exactly how many tiles?
$\displaystyle \frac{72}{24}=3$
Therefore for every tile crossed along the short side, the line will cross exactly 3 along the long side.
Hence it will cross 24(3) = 72 tiles from corner to opposite corner.