Question

What is the length and width of a rectangle if your area is 40 inches and you perimeter is 26 inches

Answer 1

l=8in or 5in
Perimeter: 26 in
Area:40 in'2

Answer 2

We can write equations, using x and y as the length and width:

xy=40
2x+2y=26

Divide the second equation by two to get:
xy=40
x+y=13

Thus, x=13-y.

We now have (13-x)x=40, so
$13x-x^2=40$
and $x^2-13x+40=0$

Factoring, we get:
(x-5)(x-8)=0

So, x can be either 5 or 8 (and y will be the other option).  Thus, the length and width are 8 and 5.