A rectangular garden 50 m. long and 34 m. Wide is surrounded by a uniform dirt road. Find the width of the road if the total area of the garden and road is 4292 m^2.

Answer 1

garden: 1700 m^2
total: 4292 m^2
road: 2592 m^2

If the road has width w, its area is

2(50w + 34w) not counting the corners, which have area w^2 each. So,

2(50w+34w)+4w^2 = 2592
4w^2 + 168w - 2592 = 0
w^2 + 42w - 648 = 0
(w+54)(w-12) = 0

so, the road is 12 ft wide.