question_answer

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

Answer:

According to condition,

Perimeter of square field = Perimeter of rectangular field

\[\Rightarrow \]   \[4\times side=2\left( l+b \right)\]

\[\Rightarrow \]   \[4\times 60=2\left( 80+b \right)\]

\[\Rightarrow \]   \[\frac{240}{2}=80+b\]

\[\Rightarrow \]   \[120-80\text{ }=b\]

\[\Rightarrow \]   40 =b

\[\therefore \]Breadth of rectangular field b = 40 m.

Area of square field = (side)2

\[={{\left( 60 \right)}^{2}}=\text{ }3600\,{{m}^{2}}\]

Area of rectangular field \[=\text{ }I\times b\]

\[=\text{ }80\times 40=3200\text{ }{{m}^{2}}\]

\[\therefore \] Square field has larger area.