Question

A footpath of uniform width runs all around the inside of a rectangular field of 38 m long and 32 m wide

Answer 1

Answer:

breadth of the rectangular field is 2 m.

Step-by-step explanation:

Sol: Outer length of the rectangular field = 32 m Outer breadth of the rectangular field = 24 m Outer Area = 32 x 24 = 768 m2 Let the width of the path be 'w' meters Inner length of the rectangular field = (32 - 2w) m Inner breadth of the rectangular field = (24 - 2w) m Inner area = (32 - 2w)(24 - 2w) = 4w2 - 112 w + 768 Area of the path = Outer area - Inner area = (768) - (4w2 - 112 w + 768) = 208 ⇒ 4w2 - 112 w + 208 = 0 ⇒ w2 - 28 w + 52 = 0 ⇒ (w - 26)(w - 2) = 0 ⇒ w = 26 or 2 Since the outer breadth of the field is 24 m, breadth of the rectangular field is 2 m.

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