Question 202338
Let the path width = x meters.
The area of the pool and path combined can be expressed by:
{{{A = (10+2x)(20+2x)}}}
{{{A = 200+60x+4x^2}}} and this is equal to 600 sq.meters., so we substitute {{{A = 600}}} and rearrange the equation a bit.
{{{4x^2+60x+200 = 600}}} Now subtract 600 from both sides to get it into standard form for a quadratic equation.
{{{4x^2+60x-400 = 0}}} Factor out a 4 to ease the calculations a bit.
{{{4(x^2+15x-100) = 0}}} So we now have:
{{{x^2+15x-100 = 0}}} Factor this quadratic equation.
{{{(x-5)(x+20) = 0}}} Applying the zero product rule, we get:
{{{x = 5}}} or {{{x = -20}}} Discard the negative solution as the path width, x, must be a positive value.
The width of the path is 5 meters.
Check:
{{{600 = (10+2x)(20+2x)}}} Substitute x = 5 meters.
{{{600 = (10+10)(20+10)}}}
{{{60 = (20)(30)}}}
{{{600 = 600}}} OK!