Question 186874
given:
{{{15*11 = 165}}} ft2 = The area of the garden
If the gravel path is of uniform width, it will
extend the width of the garden by {{{2x}}}
and it will extend the length of the garden
by {{{2x}}} also. 
So, the area of garden + path = 
{{{(15 + 2x)*(11 + 2x)}}}
Also I know area of garden + path = 
{{{165 + 192 = 357}}}, so
{{{(15 + 2x)*(11 + 2x) = 357}}}
{{{165 + 22x + 30x + 4x^2 = 357}}}
Subtract {{{165}}} from both sides
{{{22x + 30x + 4x^2 = 192}}}
Rewrite the left side
{{{4x^2 + 52x = 192}}}
Divide both sides by {{{4}}}
{{{x^2 + 13x = 48}}}
{{{x^2 + 13x - 48 = 0}}}
Use the quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 1}}}
{{{b = 13}}}
{{{c = -48}}}
{{{x = (-13 +- sqrt( 13^2-4*1*(-48) ))/(2*1) }}}
{{{x = (-13 +- sqrt( 169 + 192 ))/2 }}}
{{{x = (-13 +- sqrt( 361 ))/2 }}}
{{{x = (-13 +- 19)/2 }}}
{{{x = 3}}}
{{{x = -16}}} (not useful here)
The path can be 3 feet wide
check answer:
{{{(15 + 2x)*(11 + 2x) = 357}}}
{{{(15 + 2*3)*(11 + 2*3) = 357}}}
{{{(15 + 6)*(11 + 6) = 357}}}
{{{21*17 = 357}}}
{{{357 = 357}}}
OK