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

Given:
Length of rectangle = l = 80 cm
side of square = a = 60 cm

Also, we know
Perimeter of rectangle = 2(l + b)
Area of rectangle = lb,
where l = length and b = breadth

Perimeter of square = 4a
area of square = a²  ,
where a is side of square.
Let breadth of the rectangle be b

∵ Perimeter of the rectangle = Perimeter of the square

∴ 2 × (80 + b) = 4 × 60
2 × (80 + b) = 240

(80 + b) = 240/2
80 + b = 120

b = 120 - 80

⇒ b = 40 m

Now, area of square = a² = 60² = 3600 m²

And area of the rectangle = lb = 80 × 40 = 3200 m²

Clearly, area of square is greater.