question_answer 38)

A path 1 m wide is built along the border and inside a square garden of side 30 m. Find. (i) the area of the path. (ii) the cost of planting grass in the remaining portion of the garden at the rate of ` 40 per \[{{\text{m}}^{\text{2}}}\].                                            

Answer:

                Area of the square ABCD \[\text{= side  }\!\!\times\!\!\text{  side}\] \[\text{= 30 m  }\!\!\times\!\!\text{  30 m = 900 }{{\text{m}}^{\text{2}}}\] Area of the square PQRS \[\text{= side  }\!\!\times\!\!\text{  side}\] \[\text{= }\!\!\{\!\!\text{ 30 - (1+1) }\!\!\}\!\!\text{  m }\times \{30-(1+1)\text{ }\!\!\}\!\!\text{  m}\] \[\text{= 28 m  }\!\!\times\!\!\text{  28 m = 784 }{{\text{m}}^{\text{2}}}\] (i) Area of the path = Area of the square ABCD ? Area of the square PQRS   \[\text{= 900 }{{\text{m}}^{\text{2}}}\text{- 784 }{{\text{m}}^{\text{2}}}\text{ = 116}{{\text{m}}^{\text{2}}}\] (ii) Cost of the planting grass in the remaining portion of the garden at the rate of ` 40 per \[{{\text{m}}^{\text{2}}}\] = `\[\text{784}\times \text{4}0=\] ` 31360