The original lay of a rectangular plot ABCD on open ground is 80 m long along AB, and 69 m wide along BC. Concreted pathways are intended to be laid on the inside of the plot all around the sides. The pathways along BC and DA are each 4 M wide. The pathways along AB and DC will mutually be of equal widths such that the un-concreted internal plot will measure three-fourth of the original area of the plot ABCD. What will be the widths each of these pathways along AB and DC?
- A3m
- B4m
- C5m
- D6m
Explanation
Total area = 80 × 69 = 5,520 sq m; the inner plot must be 3/4 × 5,520 = 4,140 sq m. With 4 m paths along BC and DA, inner width = 69 − 8 = 61 m, so inner length = 4,140 ÷ 61 ≈ 67.9 m, giving a path width of (80 − 67.9)/2 ≈ 6 m — and 68 × 61 = 4,148 ≈ 3/4 of the total. Hence (D).