Question

Question 1
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

Given: The side of a square = 60 m
And the length of rectangular field = 80 m
According to question,
Perimeter of rectangular field = Perimeter of square field
$\Rightarrow 2(l\times b)=4\times side\Rightarrow 2(80+b)=4\times 60\Rightarrow 160+2b=240\Rightarrow 2b=240-160\Rightarrow 2b=80\Rightarrow b=40m$
Now Area of Square field = $(side{)}^2=(60{)}^2=3600m^2$
And Area of Rectangular field = $length\times breadth=80\times 40=3200m^2$
Hence, area of square field is larger.