Question

A pool measuring 10 meters by 20 meters is surrounded by a path of uniform width. if the area of the pool and the path combined is 600 square meters, what is the width of the path?

Answer 1

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!