Question 29162
Let the width of the paths be x meters.
The combined area of the two paths can be written:
{{{40x + 30x - x^2 = 325}}} The subtraction of{{{x^2}}} takes into account the overlapping area of the paths' intersection which would otherwise be counted twice. So now you need to solve the quadratic equation:
{{{x^2 -70x + 325 = 0}}} Factor.
{{{(x-65)(x-5) = 0}}} Apply the zero products principle.
{{{(x-65) = 0}}} and/or {{{(x-5) = 0}}}
If {{{x-65 = 0}}} then {{{x = 65}}} Discard this solution as the path can't be wider than the garden.
If {{{x-5 = 0}}} then {{{x = 5}}} This solution is valid.
The width of the path is 5 meters.