Problem: Rectangular Dimensions

If a rectangle has a length that is 3 feet less than four times its width and its perimeter is 19 feet, what are the dimensions?

Solution
We wish to determine the number of feet in each dimension of the rectangle.

$\mathbf{w:}$  the number of centimeters in the width of the rectangle
$\mathbf{4w-3:}$  the number of centimeter in the length of the rectangle
 

Draw a Diagram

The perimeter of the rectangle is the total distance around it. Therefore the number of feet in the perimeter can be represented by either $w + (4w - 3) + w + (4w - 3)$ or $19$; thus we have the equation:

$w + (4w - 3) + w + (4w - 3) = 19$
                                  $10w - 6 =19$
                                       $10w = 25$
                                  $W = \frac{2}{5}$           

AND

                                      $4w - 3 = 4^2$
                                                  $=7$


Hence the width of the rectangle is $\frac{2}{5}$ feet and the length is 7 feet.
 

Check 

The perimeter is $(\frac{2}{5} + 7 + \frac{2}{5} +7)$ feet, which equals 19 feet.