Question 68989
<pre><font size = 5><b>the length of a rectangle is 4m more than the width.
The area is 30m squared. Find the width and length.

Let the width be x

>>...the length...is 4m more than the width...<<

So the width = x + 4
 ___________
|   x + 4   |
|          x| 
|___________|
  
           A = (length)(width)
          30 = (x + 4)(x)
    x(x + 4) = 30
     x² + 4x = 30
x² + 4x - 30 = 0

That doesn't factor, so we use the quadratic formula:

            x² - 6x + 4 = 0

Use the quadratic formula:
                  ______ 
            -b ± <font face = "symbol">Ö</font>b²-4ac
        x = —————————————
                2a 

where a = 1; b = 4; c = -30

                     ______________ 
             -(4) ± <font face = "symbol">Ö</font>(4)²-4(1)(-30)
        x = ————————————————————————
                     2(1) 
                   ______ 
             -4 ± <font face = "symbol">Ö</font>16+120
        x = ——————————————
                  2

                   ___ 
             -4 ± <font face = "symbol">Ö</font>136
        x = ———————————
                 2

                   ____ 
             -4 ± <font face = "symbol">Ö</font>4·34
        x = ————————————
                 2 

                    __
             -4 ± 2<font face = "symbol">Ö</font>34
        x = ———————————
                 2

                      __
             -4     2<font face = "symbol">Ö</font>34
        x = ———— ± ——————
              2      2
                  __
        x = -2 ± <font face = "symbol">Ö</font>34 
                       __
Using the +, x = -2 + <font face = "symbol">Ö</font>34, which
is one solution and equals about 3.830951895
                       __ 
Using the -, x = -2 - <font face = "symbol">Ö</font>34, which
is the other solution and equals about
-7.830951895.
However we discard this since a rectangle's sides 
aren't negative!

So width = x = 3.830951895, and length = x + 4 =
3.830951895 + 4 = 7.830951895

Edwin</pre>