### Brain Teasers

# Rectangles

If you were to construct a 7 x 7 checkered square (i.e., a 7 x 7 chess board), how many rectangles would there be in total? You need to include squares too because a square is a special kind of rectangle.

### Hint

All the rectangles on the board can be identified by connecting:2 points of the 8 in the top edge (to form the length of the rectangle) and

2 points of the 8 in the left edge (to form the breadth of the rectangle).

### Answer

Length of rectangle and number of Possibilities7 units 1

6 units 2

5 units 3

... ...

1 unit 7

So, number of possibilities for different lengths of rectangles = 1 + 2 + 3 + ... + 7 = 28.

Similarly, number of possibilities for different breadths of rectangles = 1 + 2 + 3 + ... + 7 = 28.

Hence, number of rectangles = 28 x 28 = 784.

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