Question 83
Let $n$ be a positive integer.
a) A side square $n$ is divided into $n^{2}$ squares of unit sides by lines parallel to its sides. Determine the number of rectangles whose vertices are vertices of squares and which have sides parallel to the sides of the original square.
b) Three squares of side $n$ are arranged as in the following figure and each is divided into $n^{2}$ squares of unit sides by lines parallel to their sides. Determine the number of rectangles whose vertices are vertices of squares and which have sides parallel to the sides of the three original squares.
a) A side square $n$ is divided into $n^{2}$ squares of unit sides by lines parallel to its sides. Determine the number of rectangles whose vertices are vertices of squares and which have sides parallel to the sides of the original square.
b) Three squares of side $n$ are arranged as in the following figure and each is divided into $n^{2}$ squares of unit sides by lines parallel to their sides. Determine the number of rectangles whose vertices are vertices of squares and which have sides parallel to the sides of the three original squares.