question_answer

The length of a rectangular field is 8 m and breadth is 2 m. If a square field has the same perimeter as this rectangular field, find which field has the greater area.

Answer:

Given, length of a rectangular field = 8 m Breadth of a rectangular field = 2 m Now, perimeter of rectangular             \[=2\times (length+Breadth)\]             \[=2\times (8+2)=2\times 10\]             \[=20\,m\]                                                                                                                                             \[\therefore \] Area of rectangular field = length \[\times \] breadth      \[=8\times 2=16\text{ }{{m}^{2}}\] According to the question.                                                                                                                        Perimeter of square = perimeter of rectangular field \[\Rightarrow \] \[4\times side=20\] \[\Rightarrow \] \[\frac{4\times side}{4}=\frac{20}{4}\]                                                                                                                              [Dividing both sides by 4] side = 5m Now, area of square \[=side~\times side\]        \[=5\times 5=25\text{ }{{m}^{2}}\] Hence, the area of square field is greater than the area of rectangular field.