Question

Find the area and perimeter of a square plot of land whose diagonal is 24 m long. $\left[\mathrm{Take}\sqrt{2}=1.41\right]$

Answer 1

Area of the square = $\frac{1}{2}\times {\mathrm{Diagonal}}^2$

=$\frac{1}{2}\times 24\times 24$
=$288{\mathrm{m}}^2$
Now, let the side of the square be x m.
Thus, we have:
$$\begin{gathered} \mathrm{Area}={\mathrm{Side}}^2 \\ \Rightarrow 288=x^2 \\ \Rightarrow x=12\sqrt{2} \\ \Rightarrow x=16.92 \end{gathered}$$

Perimeter = $4\times \mathrm{Side}$
$$\begin{gathered} =4\times 16.92 \\ =67.68\mathrm{m} \end{gathered}$$

Thus, the perimeter of the square plot is 67.68 m.