question_answer

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