Question 82346
Let W=width of rectangle
Then length=4W+1

Area(A) of rectangle=Length*Width=W*(4W+1)

Now we are told that:
 W*(4W+1)=72  get rid of parens

4W^2+W=72  subtract 72 from both sides

4W^2+W-72=72-72 or

4W^2+W-72=0   quadratic in standard form.  We'll use the quadratic formula:

{{{W = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 

{{{W = (-1 +- sqrt( 1^2-4*4*(-72) ))/(2*4) }}} 

{{{W = (-1 +- sqrt(1153))/(8) }}} 

{{{W = (-1 +sqrt (1153))/(8) }}} 


{{{W = 4.120}}} cm ----------------------width of rectangle

{{{4W+1=4(4.120)+1=17.480}}} cm---------------------length of rectangle

Discount negative value for W. Lengths are positive.

CK

A=L*W=(4.120)(17.480)=72 cm^2

~72 cm^2=72 cm^2


Hope this helps----ptaylor