Question

Two plots of land have the same perimeter. One is square of side $50m.$while the other is a rectangle whose length is $60m.$Which plot has the greater area and by how much?

Answer 1

Here, the length of the side of the square $=50m$

So, the area of square $=50\times 50m^2$

$=2500m^2$

perimeter of square $=4\times 50m$

$=200m$

So, the perimeter of a rectangle $=200m$

Here, the length of a rectangle $=60m$

let the breadth be$x$.

So, the perimeter of a rectangle $=2\times (60+x)$

$=120+2x$

So,

$$\begin{gathered} 120+2x=200 \\ \Rightarrow 2x=200-120 \\ \Rightarrow 2x=80 \\ \Rightarrow x=\frac{80}{2} \\ \Rightarrow x=40 \end{gathered}$$

So, breadth $=40m$

So, the area of a rectangle $=60\times 40$

$=2400m^2$

Hence, the Area of the square is greater than the rectangle.