A rectangular plot of land measures 95 m by 72 m. Inside the plot, a path of uniform width of 3.5 m is to be constructed all around. The rest of the plot is to be laid with grass. Find the total expenses involved in constructing the path at Rs 80 per m² and laying the grass at Rs 40 per m².

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Solution

Let PQRS be the given rectangular plot and ABCD be the inside boundary of the path.

Length = 95 m
Breadth = 72 m
Area of the plot = (95 $\times$ 72) m² = 6,840 m²
Width of the path = 3.5 m
∴ AB = (95 - 2 $\times$ 3.5) m = (95 - 7) m = 88 m
AD = (72 - 2 $\times$ 3.5) m = (72 - 7) m = 65 m
Area of the grassy rectangle plot ABCD = (88 $\times$ 65) m² = 5,720 m²
Area of the path = (Area PQRS - Area ABCD)
= (6840 - 5720) m² = 1,120 m²
Rate of constructing the path = Rs. 80 per m²
∴ Total cost of constructing the path = Rs. (1,120 $\times$ 80) = Rs. 89,600
Rate of laying the grass on the plot ABCD = Rs. 40 per m²
∴ Total cost of laying the grass on the plot = Rs. (5,720 $\times$ 40) = Rs. 2,28,800
∴ Total expenses involved = Rs. ( 89,600 + 2,28,800) = Rs. 3,18,400

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A rectangular plot of land measures 95 m by 72 m. Inside the plot, a path of uniform width of 3.5 m is to be constructed all around. The rest of the plot is to be laid with grass. Find the total expenses involved in constructing the path at Rs 80 per m2 and laying the grass at Rs 40 per m2.

A rectangular plot of land measures 95 m by 72 m. Inside the plot, a path of uniform width of 3.5 m is to be constructed all around. The rest of the plot is to be laid with grass. Find the total expenses involved in constructing the path at Rs 80 per m² and laying the grass at Rs 40 per m².