Question

A rectangle has an area of 256 cm 2 width 48 cm shorter than 4 times its length. what is the rectangle's length?

Answer 1

If we let x represent the length, then the width is (4x-48), and the area is ...
  x(4x-48) = 256

This is neatly solved graphically to find x = 16. (x=-4 is an extraneous solution)

The rectangle's length is 16 cm.

Answer 2

To find area, we use this equation:
L×W=A
We already know what the Area is so let's fill it in.
L×W=256
The question says that the width is 48 cm shorter than 4 times its length.
W=4L-48
We can put that equation in for width.
(4l-48)l=256 ;let's multiply.
4l²-48l=256
To find this, you can use a graph as shown below.
So, the rectangle's length is 16 cm.