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in Perimeter and Area of Plane Figures by (30.3k points)
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A footpath of uniform width runs all around the inside of a rectangular field 54m long and 35 m wide. If the area of the path is 420m2, find the width of the path.

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Area of the rectangular field = 54 x 35 = 1890m2.

Let the width of the path be x m. The path is shown in the following diagram:

Length of the park excluding the path = (54 - 2x)m

Breadth of the park excluding the path = (35 - 2x)m

Thus, we have:

Area of the path = 420 m2

The width of the path cannot be more than the breath of the rectangular field.

∴ x = 2.5 m

Thus, the path is 2.5 m wide.

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