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

We know that Perimeter of square=\(4\times side=4\times 60=240m\)
Also, we have perimeter of rectangle=2(l+b)

Given that these both have same parimeter.

Therefore, we can say that:

perimeter of rectangle=Perimeter of square

\(2(l+b)=240\)

\(\Rightarrow 2(80 + b) = 240\)

\(\Rightarrow 160+2b = 240\)

\(\Rightarrow 2b=240-160=80\)

\(\Rightarrow b=40m\)

Hence we have, Area of figure (a) i.e, square =\( (side)^2\) = \(60 \times 60 = 3600 m^2\)

Area of figure (b) i.e, rectangle =\( l \times b = 80 \times 40 = 3200 m^2\)

So, the area of figure (a) i.e, square is more than the area of figure (b) i.e, rectangle.