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A path of uniform width turns the inside of a rectangular field 38m long and 32m wide. IF the path occupies 600 m2 than the width of the path is_______?

Correct answer: B. 5m

  • A. 3m
  • B. 5m
  • C. 8.75m
  • D. 10m

Explanation

If the path has width w metres inside the field, its area is 38 m × 32 m minus (38 − 2w) m × (32 − 2w) m. Setting this equal to 600 square metres gives 1216 − (1216 − 140w + 4w²) = 600, or w² − 35w + 150 = 0, so w = 5 m or 30 m; only 5 m fits inside the 32 m width. The likely mistake is accepting 30 m, the algebraic root that is physically impossible for an internal path.

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Area measures the surface enclosed by two-dimensional figures, while volume measures the space occupied by three-dimensional solids. Problems use formulas for rectangles, triangles, circles, prisms, cylinders, cones, spheres, and composite figures, including unit conversion and the distinction between surface area, lateral area, and volume.

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