Question 26465
Let the width of the walkway = x ft.
The total area, A, of the garden plus walkway can be expressed in terms of x as follows: A = L*W

{{{A = (40+2x)(30+2x)}}} Perform the indicated multiplication.
{{{A = 1200+140x+4x^2}}} The total area is given as 8000 sq.ft., so:
{{{1200+140x+4x^2 = 8000}}} Subtract 8000 from both sides of the equation.
{{{4x^2+140x-600 = 0}}} Solve this quadratic equation for x. First factor out a 4.
{{{4(x^2+35x-150) = 0}}} Apply the zero products principle.
{{{x^2+35x-150 = 0}}} Solve using the quadratic formula: {{{x = (-b+-sqrt(b^2-4ac))/2a}}}
{{{x = (-35+-sqrt(35^2-4(1)(-150)))/2(1)}}}
{{{x = (-35+-sqrt(1225+600))/2}}}
{{{x = (-35+-sqrt(1825))/2}}}
{{{x = (-35-42.72)/2}}} = -38.86 Discard this negative solution.
{{{x = (-35+42.72)/2}}} = 3.86 ft.

The walkway is 3.86 feet wide.