a rectangular plot of ground having dimensions 46 feet by 30 feet is surrounded by a walk of uniform width. If the area of the walk is 240 ftˆ2, what is its width?

Answer 1

area w/o walk: 46*30 = 1380
area w/walk (46+2w)(30+2w)

So, we have

(46+2w)(30+2w) - 1380 = 240
4w^2 + 152w + 1380 - 1380 = 240
4w^2 + 152w - 240 = 0
w^2 + 38w - 60 = 0
w = -19 + sqrt(421) = 1.5