Question

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

(a) (b)

Answer 1

Finding the area of given fields:

Side of a square $s=60m$

Length,$l=80m$

According to the given details,

Perimeter of rectangular field $=$ perimeter of square field

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

$$\begin{gathered} \Rightarrow 2\times (80+b)=4\times 60 \\ \Rightarrow 160+2b=240 \\ \Rightarrow b=40 \end{gathered}$$

Thus, breadth of the rectangle is $40m$

Area of square field $={\mathrm{s}}^2={60}^2=3600{\mathrm{m}}^2$

And Area of rectangular field $=$length $\times$breadth $=80\times 40=3200m^2$

Hence, area of square field is larger.