Question

A footpath of uniform width runs round the inside of a rectangular field 32 m long and 24 m wide. If the path occupies 208 m², find the width of the footpath.

Answer 1

Let w be the width of the footpath.

Area of the path = Area of outer rectangle – Area of inner rectangle

∴ 208 = (32)(24) – (32 – 2w)(24 – 2w)

208 = 768 – 768 + 64w + 48w – 4w²

4w² – 112w + 208 = 0

w² – 28w + 52 = 0

w² – 26w – 2w + 52 = 0

w(w – 26) – 2(w – 26) = 0

(w – 26)(w – 2) = 0

w = 26, 2

If w = 26, then breadth of inner rectangle = (24 – 52) m = –28 m, which is not possible.

Hence, the width of the footpath is 2 m.