Question 71134
Let x=width of sidewalk

Then (60-2x) and (80-2x) would be new dimensions of parking lot

And (60-2x)(80-2x) would be new area of parking lot
Also (60)(80)=4800 sq ft= old area


Now we are told that the new area is 2/3 that of the old area.  So our equation to solve is:

(60-2x)(80-2x)=(2/3)(4800)  get rid of parens
4800-280x+4x^2=3200  subtract 3200 from both sides

4800-3200-280x+4x^2=3200-3200  collect like terms:

4x^2-280x+1600=0  divide all terms by 4

x^2-70x+400=0

We'll solve using the quadratic formula:

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{x = (70 +- sqrt( 4900-1600 ))/(2) }}} 
{{{x = (70 +- ( 57.446 ))/(2) }}}
x =6.277 ft------------------------------correct ans
 and
x=63.723 ft--------------------------------impossible ans


CK


2x=2(6.277)=12.554

(60-12.554)(80-12.554)=3200

(47.446)(67.446)=3200

3200=3200