Question

Find the length of the diagonal of a square whose area is 128 cm². Also, find its perimeter.

Answer 1

Area of the square = 128 cm²
$$\begin{gathered} \mathrm{Area}=\frac{1}{2}{d}^2(\mathrm{where}d\mathrm{is}\mathrm{a}\mathrm{diagonal}\mathrm{of}\mathrm{the}\mathrm{square}) \\ \Rightarrow 128=\frac{1}{2}{d}^2 \\ \Rightarrow d^2=256 \\ \Rightarrow d=16\mathrm{cm} \end{gathered}$$

Now,
Area = ${\mathrm{Side}}^2$
$$\begin{gathered} \Rightarrow 128={\mathrm{Side}}^2 \\ \Rightarrow \mathrm{Side}=11.31\mathrm{cm} \end{gathered}$$

Perimeter = 4(Side)
$$\begin{gathered} =4\left(11.31\right) \\ =45.24\mathrm{cm} \end{gathered}$$
Thus, the perimeter of the square is 45.24 cm.