Question

If perimeter of a rectangle is `56` and that length and breadth are integers, how many rectangles can be formed?

Answer 1

14 rectangles assuming that length and breadth are integers. However, if length and breadth can take any positive real value we can infinite rectangles.

Explanation:

We know perimeter of rectangle = 2*(length + breadth) unit.

Here, 2*(length + breadth) = 56 cm

So, (length + breadth) = 56/2 = 28

Now assuming that length and breadth can only be integers ,

28 = (27+1), (26+2), (25+3),............. (1+27).

So, there will be 27 rectangles which can be drawn, but observe that 27+1 is same as 1+27, hence 14 rectangles.

However, if length and breadth can take any positive real value so that (length + breadth) = 28, we can infinite rectangles .