Question

How many rectangles have a perimeter of 100

Answer 1

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 )