Question

The area of a square field is 36 m². A path of uniform width is laid around and outside of it. If the area of the path is 28 m², then find the width of the path.

Answer 1

$$\begin{gathered} \mathrm{As},\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{square}\mathrm{field}=36{\mathrm{m}}^2 \\ \mathrm{So},\mathrm{the}\mathrm{side}\mathrm{of}\mathrm{the}\mathrm{square}\mathrm{field}=\sqrt{36}=6\mathrm{m} \\ \mathrm{Also},\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{outer}\mathrm{square}=\mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{square}+\mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{path} \\ =36+28 \\ =64{\mathrm{m}}^2 \\ \mathrm{So},\mathrm{the}\mathrm{side}\mathrm{of}\mathrm{the}\mathrm{outer}\mathrm{square}=\sqrt{64}=8\mathrm{m} \\ \mathrm{Now},\mathrm{the}\mathrm{width}\mathrm{of}\mathrm{the}\mathrm{path}=\frac{\mathrm{Side}\mathrm{of}\mathrm{the}\mathrm{outer}\mathrm{square}-\mathrm{Side}\mathrm{of}\mathrm{the}\mathrm{inner}\mathrm{square}}{2} \\ =\frac{8-6}{2} \\ =\frac{2}{2} \\ =1\mathrm{m} \end{gathered}$$

So, the width of the path is 1 m.