Question 256203
First draw a rectangle and label it 10m on the length and 50m on the width.
Second draw a rectangle around the pool and place an x to the left and right of the 10 and above and below the 50.
step 1 - area of pool.
A = LW = 10*50 = 500
step 2 - area of pool +  walkway = 864
(i) A = {{{(10+2x)(50+2x) - 500 = 864}}}
(ii) A = {{{(4x^2+120x+500) - 500 = 864}}}
(iii) A = {{{4x^2+120x = 864}}}
setting = 0, we get
(iv) {{{4x^2 + 120x - 864 = 0}}}
dividing by 4 and then factoring, we get
(vi) {{{(x-6)(x+36) = 0}}}
So,
x = 6 or x = -36.
width of the walk is 6m.