Question

A given rectangle has an area of 20 ft.². What is the length for various widths?

Answer 1

well, the area of a rectangle is simply length * width, just that product, this one has an area of 20.

now, if we do a quick prime factoring of 20, we get 20 = 2 * 2 * 5.

so we can shuffle around those numbers like

$\bf \stackrel{length}{\stackrel{(2\cdot 2)}{(4)}}\times\stackrel{width}{(5)}\qquad\qquad\qquad \stackrel{length}{(2)}\times\stackrel{with}{\stackrel{(2\cdot 5)}{(10)}}$