Question

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.

Answer 1

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.