Question

how many different rectangles can you make with the 24 cm long string with integral sides and what are the sides of those rectangles in centimetres

Answer 1

With a 24 cm string you need to have 2 lengths and 2 widths covered.

2(l+w)=24.  

So l+w=12.  

The set of length and widths that satisfy this are (11,1),(10,2),(9,3),(8,4),(7,5),(6,6).  

The last one will turn out to be a square a specific case of rectangle :)