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

Let the side of square field be $a=60m$

Let the length of the rectangular field be $l=80m$ and breadth be $bm$.

According to the question,

perimeter of square $=$ Perimeter of rectangle

$4\times a=2(l+b)$

$\Rightarrow 4\times 60=2(80+b)$

$\Rightarrow 240=160+2b$

$\Rightarrow 2b=80$

$\Rightarrow b=40$

Area of square $=a^2=60\times 60=3600m^2$

Area of rectangle $=l\times b=80\times 40=3200m^2$

So, the area of the square is greater than the area of the rectangle.