A circular plot of ground of radius 42 meters is surrounded by a ring of grass plot. Find the width of the grass plot, if its area is equal to that of circular plot.

Suppose the width of the grass plot is r.
Radius of circular plot = 42 m

So, area of circular plot of radius 42 m = $\mathrm{\pi }{\left(42\right)}^2$
And radius of plot including surrounded grass plot = (42 + r)
Then, area of plot including grass plot = $\mathrm{\pi }{\left(42+\mathrm{r}\right)}^2$
So, area of grass plot = area of plot including grass plot  - area of circular plot of radius 42 m
= $\mathrm{\pi }{\left(42+\mathrm{r}\right)}^2-\mathrm{\pi }{\left(42\right)}^2$
According to the question, area of grass plot is equal to the area of circular plot of radius 42 m, so we have;
$$\begin{gathered} \mathrm{\pi }{\left(42+\mathrm{r}\right)}^2-\mathrm{\pi }{\left(42\right)}^2 = \mathrm{\pi }{\left(42\right)}^2 \\ \Rightarrow \mathrm{\pi }{\left(42+\mathrm{r}\right)}^2 = 2 \mathrm{\pi }{\left(42\right)}^2 \\ \Rightarrow {\left(42+\mathrm{r}\right)}^2 = 2\times {\left(42\right)}^2 \\ \Rightarrow \left(42+\mathrm{r}\right) = \sqrt{2\times {\left(42\right)}^2} \\ \Rightarrow \left(42+\mathrm{r}\right) = 42\sqrt{2} \\ \Rightarrow \mathrm{r} = 42\sqrt{2}-42 = 42\times 1.41-42 = 17.22 \end{gathered}$$
Therefore, width of grass plot is 17.22 m.