question_answer 34)

A garden is 90 m long and 75 m broad. A path 5 m wide is to be built outside and around it. Find the area of the path. Also find the area of the garden in hectare.

Answer:

                Area of the garden ABCD \[\text{ }l\times b\]                                  \[\text{= 90 m  }\!\!\times\!\!\text{  75 m = 6750 }{{\text{m}}^{\text{2}}}\]                 \[=\frac{6750}{10000}\text{ hectare = 0}\text{.675 hectare}\] Area of the rectangle \[\text{PQRS}=l\times b\] \[\text{= (90 + 5 + 5) m  }\!\!\times\!\!\text{  (75 + 5 + 5) m}\] \[\text{= 100 m  }\!\!\times\!\!\text{  85 m = 8500 }{{\text{m}}^{\text{2}}}\] \[=\frac{8500}{10000}\text{ hectare}\] \[\text{= 0}\text{.850 hectare}\] \[\therefore \]                  Area of the path = Area of the rectangle PQRS ? Area of the rectangle ABCD \[=0.\text{85}0\text{ hectare}-0.\text{675 hectare or 85}00-\text{6750 }{{\text{m}}^{\text{2}}}\] \[\text{= 1750 }{{\text{m}}^{\text{2}}}\text{or 0}\text{.175 hectare}\text{.}\]