Question 27771
Let the width of the path be x meters. You can express the combined area in terms of x:

{{{A = (25+2x)(40+2x)}}} and this is given as 1,426 square meters, so:
{{{(25+2x)(40+2x) = 1426}}} Simplify and solve for x.
{{{1000+130x+4x^2 = 1426}}} Subtract 1426 from both sides of the equation.
{{{4x^2+130x-426 = 0}}} Solve this quadratic equation by factoring. First, factor out a 2.
{{{2(2x^2+65x-213) = 0}}} Apply the zero products principle.
{{{2x^2+65x-213 = 0}}} Factor this.
{{{(2x+71)(x-3) = 0}}} Apply the zero products principle.
{{{(2x+71) = 0}}} and/or {{{(x-3) = 0}}}
If{{{2x+71 = 0}}} then {{{2x = -71}}} and {{{x = -35.5}}} Discard this solution as the path width must be a positive number.
If {{{x-3 = 0}}}, then {{{x = 3}}}

The width of the path is 3 meters