A path 1 m wide is built along the border inside a square garden of side 30 m. Find |
(a) The area of the path, |
(b) The cost of planting grass in the remaining portion of the garden at the rate of Rs 40 per\[{{m}^{2}}\]. |
Answer:
Let ABCD be a square garden, and let PQRS be the internal boundary of the path. We have, AB = 30 m and, PQ = (30 ? 1 ? 1) m = 28 m (a) The area of the path = Area of square ABCD \[-Area\text{ }of\text{ }square\text{ }PQRS\] \[=\left( {{30}^{2}}{{28}^{2}} \right){{m}^{2}}\] \[=\left( 30+28 \right)\left( 3028 \right){{m}^{2}}\] \[=\left( 58\times 2 \right){{m}^{2}}=116{{m}^{2}}\] (b) Area of the remaining portion of the garden = Area of square PQRS \[=\left( 28\times 28 \right){{m}^{2}}=784{{m}^{2}}\] Cost of planning the grass in PQRS at the rate of Rs 40 per \[{{m}^{2}}\] = Rs (40 × 784) = Rs 31,360 2
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