#### 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 – 4w^{2}

4w^{2} – 112w + 208 = 0

w^{2} – 28w + 52 = 0

w^{2} – 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.

Is there an error in this question or solution?

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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. Concept: Quadratic Equations.

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