Let [tex]x[/tex] be the width of the rectangle.
Since the perimeter of this rectangle is 100, then the height of the triangle must be [tex]50-x.[/tex]
Both width and height are positive numbers, so we must have
[tex]x>0~~\text{ and }~~50-x>0\\\\ x>0~~\text{ and }~~50>x\\\\ 0<x<50[/tex]
There are infinity real numbers that are greater than zero and less than 50. Therefore, there are infinity rectangles having a perimeter of 100.
[tex]\bullet~~[/tex] width: [tex]x[/tex]
[tex]\bullet~~[/tex] height: [tex]50-x[/tex]
[tex]0<x<50[/tex]
(You can pick any real number between [tex]0[/tex] and [tex]50[/tex] for the [tex]x[/tex] value )
