Question

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

• A. Square has larger area, square $=3600m^2$.
• B. Rectangle has larger area, square $=3600m^2$.
• C. Square has larger area, square $=1600m^2$.
• D. Square has larger area, square $=3800m^2$.

Answer 1

The correct option is A Square has larger area, square $=3600m^2$.

Let $x$ be the breadth of the rectangle. It is given that the perimeter of a rectangle = perimeter of the square.
$\therefore 2(80+x)=4\times 60$
$\Rightarrow 80+x=120$
$\Rightarrow x=120-80=40$
i.e. breadth of the rectangle $=40m$
Now, Area of the square $=(60\times 60)m^2=3600m^2$
and the area of the rectangle $=(40\times 80)m^2=3200m^2$.
Hence, the square field has a larger area.