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

Let the side of square field be a=60 m
Let the length of the rectangular field be l=80 m and breadth be b m.
According to the question, perimeter of square = Perimeter of rectangle
4×a = 2(l+b) ⇒ 4×60 = 2(80+b) ⇒ 240 = 160+2b ⇒ 2b = 80 ⇒ b = 40
Area of square = a² = 60×60 = 3600 m²
Area of rectangle = l×b = 80×40 = 3200 m²
So, the area of the square is greater than the area of the rectangle.