Question 895844
Total dimensions:  Using w for width of the path,

2w+10 and 2w+20.
{{{(2w+10)(2w+20)=416}}} to account for combined pool area and path area.


Simplify.
{{{2(w+5)2(w+10)=2*2*104}}}
{{{(w+5)(w+10)=104}}}
{{{w^2+15w+50=104}}}
{{{w^2+15w-54=0}}}
Discriminant, {{{15^2+4*54=441=21^2}}}
{{{w=(-15+21)/2}}}
{{{highlight(w=3)}}}


That quadratic IS factorable as (w-3)(w+18) and the equation could be solved through factoring.