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<x<50`

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<x<50`

(You can pick any real number between
`0` and
`50` for the
`x` value )