Question

A wire of length 20 m is to be folded in the form of a rectangle. How many rectangles can be formed by folding the wire if the sides are positive integers in metres ?

Answer 1

It is given that a wire of length 20 m is to be folded in the form of a rectangle; therefore, we have:
Perimeter of the rectangle = 20 m
$\Rightarrow$ 2(Length + Breadth) = 20 m
$\Rightarrow$ (Length + Breadth ) = 20/2 = 10 m

Since, length and breadth are positive integers in metres, therefore, the possible dimensions are:
(1m, 9m), (2m, 8m), (3m, 7m), (4m, 6m) and (5m, 5m)

Thus, five rectangles can be formed with the given wire.