Question

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

Answer 1

Perimeter of square = 4 (Side of the square) = 4 (60 m) = 240 m Perimeter of rectangle = 2 (Length + Breadth)

= 2 (80 m + Breadth)

= 160 m + 2 × Breadth

It is given that the perimeter of the square and the rectangle are the same. 160 m + 2 × Breadth = 240 m

Breadth of the rectangle = (80/2)m = 40 m Area of square = (Side)² = (60 m)² = 3600 m²

Area of rectangle = Length × Breadth = (80 × 40) m² = 3200 m²

Thus, the area of the square field is larger than the area of the rectangular field.