Question

Two plots of land have the same perimeter. One is a square of side $64m$ and the other a rectangle with length $80m$. Which plot has the greater area and by how much?

Answer 1

Perimeter of square $=4\times side$

$\begin{array}{c}=4\times 64\\ =256cm\end{array}$

Perimeter of Rectangle = Perimeter of square

$\begin{array}{c}\Rightarrow 2\times \left(length+breadth\right)=256\\ \Rightarrow 2\times \left(80+breadth\right)=256\\ \Rightarrow breadth=48cm\end{array}$

Area of square $=side\times side$

$\begin{array}{c}=64\times 64\\ =4096c{m}^2\end{array}$

Area of rectangle = $=l\times b$

$\begin{array}{c}=80\times 48\\ =3840c{m}^2\end{array}$

Area of Square is greater than Area of Rectangle.