question_answer 1)

                A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?                 (a)                          (b)

Answer:

                Area of the square field \[=60m\times 60m=3,600\,{{m}^{2}}\] Perimeter of the square field \[=4\times 60\text{ }m=240\text{ }m\] \[\therefore \] Perimeter of rectangular field \[=240\text{ }m\] \[\Rightarrow \]               \[2(80+x)\,=240,\] where \[x\,\,m\] is the breadth of the rectangular field                        \[\Rightarrow \]               \[80+x\,=\frac{240}{2}\]               \[\Rightarrow \]               \[80+x=120\] \[\Rightarrow \]               \[x=120-80=40\] \[\therefore \] Breadth = 40 m \[\therefore \] Area of rectangular field                 \[=l\times b=80\,m\times 40\,m=3,200\,{{m}^{2}}\] So, the square field has a larger area.