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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.
Solution
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.
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