Question

A wire of length $20m$ is be folded in the from 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) $=\frac{20}{2}=10$ m

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

Also, $(5,5)$ can be considered as a rectangle (as every square is a special type of rectangle )

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