Question

Two plots of land have the same perimeter. One is a square of side 64 m and the other is a rectangle of length 70 m. Find the breadth of the rectangular plot. Which plot has the greater area and by how much?

Answer 1

Side of the square plot = 64 m
Perimeter of the square plot = $(4\times S\mathrm{ide})\mathrm{m}=(4\times 64)\mathrm{m}=256\mathrm{m}$
Area of the square plot = (Side)²
= 64² m²
= 4096 m²

Let the breadth of the rectangular plot be x m.
Perimeter of the rectangular plot = 2(l+b) m
= 2(70+x) m

Perimeter of the rectangular plot = Perimeter of the square plot (Given)
$$\begin{gathered} \Rightarrow 2(70+x)=256 \\ \Rightarrow 140+2x=256 \\ \Rightarrow 2x=256-140 \\ \Rightarrow 2x=116 \\ \Rightarrow x=\frac{116}{2}=58 \end{gathered}$$
So, the breadth of the rectangular plot is 58 m.
Area of the rectangular plot = $(L\mathrm{ength}\times B\mathrm{readth})=(70\times 58){\mathrm{m}}^2=4060{\mathrm{m}}^2$
Area of the square plot − Area of the rectangular plot
= (4096 − 4060)
= 36 m²
Area of the square plot is 36 m² greater than the rectangular plot.