Question 180189
FIRST, DRAW THE PICTURE
Let x=width of the path
Then the outside dimensions of the rectangular garden plus path are:
Length =15+2x
Width=11+2x
Now we are told that Length*Width=192 sq ft or:
(2x+15)(2x+11)=192 expand the left side using FOIL
4x^2+22x+30x+165=192 subtract 192 from each side
4x^2+22x+30x+165-192=0  collect like terms
4x^2+52x-27=0 quadratic in standard form. Solve using the quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}=
{{{x = (-52 +- sqrt( 52^2-4*4*(-27) ))/(8) }}}=
{{{x = (-52 +- sqrt( 2704+432 ))/(8) }}}=
{{{x = (-52 +- sqrt( 3136 ))/(8) }}}=
{{{x = (-52+ or -56)/(8) }}}=
  Disregard the negative value for x. Path widths are positive:
{{{x = (-52 +56)/(8) }}}= 
{{{x = (4)/(8) }}}= 0.5 ft---width of path

CK
(12)(16)=  192
192=192


I BET YOU COULD HAVE SOLVED THE QUADRATIC!!!!!!!!!!
HOPE THIS HELPS----------PTAYLOR