A footpath of uniform width runs all around the inside of rectangular field 50m long and 38m wide. If the area of the path is 492m ^2, find its width?

Let the width of footpath=x The total area of rectangle ABCD = area of footpath + area of EFGH 50×38 = 492+[(50−2x)×(38−2x)] = 1900=492+ [1900−100x−176x+4x2] = 4×2−176x+492=0 = x2−44x+123=0 (x−3)(x−41)=0 x=3m

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