Question 95455
Let w=width

Then length (l)=4w+5  (we are told this)

Area of a rectangle =length x width. So we have

80=w(4w+5) get rid of parens

80=4w^2+5w  subtract 80 from both sides

4w^2+5w-80=80-80 or

4w^2+5w-80=0---------quadratic in standard form

Solve using the quadratic formula:

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{x = (-5 +- sqrt( 5^2-4*4*(-80) ))/(2*4) }}} 
{{{x = (-5 +- sqrt(1305))/(8)}}} 

{{{x = (-5 +- 36.125)/(8)}}} 

Disregard the negative value for x.  Lengths and widths are positive

{{{x = (-5 +36.125)/(8)}}} 
{{{x = 31.125/(8)}}} 
{{{x = 3.891}}}cm--------------------width
{{{4x+5=4(3.891)+5 = 20.562}}}cm-------------length

CK
{{{A=l*w=3.891*20.562=80.008}}} cm
~80=~80

Hope this helps---ptaylor