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