Question 827647
let x be the width of the footpath and we want to subtract the areas of two rectangles
208 = (32*24) - ((32-2x)*(24-2x))
208 = 768 - (768 -112x +4x^2)
208 = 112x -4x^2
4x^2 -112x +208 = 0
divide both sides of = by 4
x^2 -28x +52 = 0
this expression factors into
(x-2) * (x-26) = 0
we have two solutions for x, namely 2 and 26 BUT we can eliminate 26 since that value is greater than the width of the larger rectangle, now check the answer
x = 2 m
208 = 768 - (28 * 20)
208 = 768 - 560
208 = 208
answer checks