Question

The length of a rectangular field is $10m$ and breadth is $4m$. If a square field has the same perimeter as this rectangular field, find which field has the greater area.

Answer 1

Step 1: Finding the perimeter of the square and rectangle.

Given, length = $10m$, breadth = $4m$

Perimeter of rectangle = $2\times \left(length+breadth\right)$

$$\begin{gathered} =2\times \left(10+4\right) \\ =2\times 14 \\ =28m \end{gathered}$$

Given,

Perimeter of rectangle = perimeter of the square

$$\begin{gathered} \Rightarrow 28=4\times \mathrm{side} \\ \Rightarrow \frac{28}{4}=\mathrm{side} \\ \Rightarrow 7\mathrm{m}=\mathrm{side} \end{gathered}$$

Step 2: Finding the area of square and rectangle.

Area of square = $side\times side$

$$\begin{gathered} =7\times 7 \\ =49m^2 \end{gathered}$$

Area of rectangle = $length\times breadth$

$$\begin{gathered} =10\times 4 \\ =40m^2 \end{gathered}$$

Hence, as we can see the square field has the greater area.