A 115-m-long and 64-m-broad lawn has two roads at right angles, one 2 m wide, running parallel to its length, and the other 2.5 m wide, running parallel to its breadth. Find the cost of gravelling the roads at Rs 60 per m².

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Solution

Let ABCD be the rectangular field and PQRS and KLMN be the two rectangular roads with width 2 m and 2.5 m, respectively.

Length of the rectangular field, CD = 115 cm
Breadth of the rectangular field, BC = 64 m
∴ Area of the rectangular lawn ABCD = 115 m × 64 m = 7360 m²
Area of the road PQRS = 115 m × 2 m = 230 m²
Area of the road KLMN = 64 m × 2.5 m = 160 m²
Clearly, the area of EFGH is common to both the two roads.
∴ Area of EFGH = 2 m × 2.5 m = 5 m²
∴ Area of the roads = Area (KLMN) + Area (PQRS) − Area (EFGH)
= (230 m² + 160 m²) − 5 m² = 385 m²
Rate of gravelling the roads = Rs 60 per m²
∴ Total cost of gravelling the roads = Rs (385 × 60)
= Rs 23,100

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A 115-m-long and 64-m-broad lawn has two roads at right angles, one 2 m wide, running parallel to its length, and the other 2.5 m wide, running parallel to its breadth. Find the cost of gravelling the roads at Rs 60 per m2.

A 115-m-long and 64-m-broad lawn has two roads at right angles, one 2 m wide, running parallel to its length, and the other 2.5 m wide, running parallel to its breadth. Find the cost of gravelling the roads at Rs 60 per m².