Question 133683
Area(A)=Length(l) times Width(w) or A=l*w

Let w=width

Then length(l)=2w-1

Now we are told that:

w*(2w-1)=120 or
2w^2-w=120  subtract 120 from each side

2w^2-w-120=120-120   
2w^2-w-120=0 quadratic in standard form-solve using quadratic formula:

{{{w = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{w = (1 +- sqrt( 1-4*2*(-120) ))/(2*2) }}} 
{{{w = (1 +- sqrt( 1+960))/(4) }}} 
{{{w = (1 +- sqrt(961))/(4) }}} 
{{{w = (1 +-31)/(4) }}} 

Neglect the negative value for w.  In this case, length and width are positive.

{{{w=(1+31)/4=8}}} ft --- width of garden

{{{2w-1=2*8-1=15}}} ft ----length of garden

CK
A=l*w=15*8=120 sq ft

and 15=2*8-1

Hope this helps--ptaylor