Question

A square and a rectangular field with measurements as given in the figure have the same perimeter. The field with larger area is :

• A. Rectangular field
• B. Square field
• C. Both have same area
• D. All of the above

Answer 1

The correct option is B

Square field

Perimeter of Square $=4\times \text{side}=4\times 60m=240m$

$\Rightarrow$ Area of Square $=Sid{e}^2={60}^2=3600sq.m.$

$\Rightarrow$ Perimeter of Rectangle = 2(length + breadth)

Or, 240 = 2(80 + breadth)

Or, 80 + breadth = 120

Or, breadth = (120 - 80) = 40 m

Area of rectangle = length $\times$ breadth $=(80\times 40)sq.m.=3200sq.m.$

So, area of the square field is greater than that of the rectangular field.