Question:
The area of a square plot is $101 \frac{1}{400} \mathrm{~m}^{2}$. Find the length of one side of the plot.
Solution:
Let length of the square plot be a. Then, the area of square $=a^{2}$ According to the question,
Area $=101 \frac{1}{400} \mathrm{~m}^{2}$ [given]
$\therefore$ $a^{2}=101 \frac{1}{400} \Rightarrow a^{2}=\frac{40401}{400}$
$\Rightarrow$ $a=\sqrt{\frac{40401}{400}} \Rightarrow a=\sqrt{\frac{201 \times 201}{20 \times 20}}$
$\therefore$ $a=\frac{201}{20}=10 \frac{1}{20} m$ [taking square root on both sides]
Hence, the length of one side of the piot is $10 \frac{1}{20} \mathrm{~m}$.