Question

The area of a square filed is 64 m². A path of uniform width is laid around and outside of it.
If the area of the path is 17 m², then the width of the path is

(a) 1 m (b) 1.5 m (c) 0.5 m (d) 2 m

Answer 1

Let a be the side of inner square. Then
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{inner}\mathrm{square}=a^2 \\ \Rightarrow 64=a^2\Rightarrow a=\sqrt{64}=8\mathrm{cm} \end{gathered}$$
Let x be the width of the path, then
Side of outer square = (a + x) cm = (8 + x) cm
Now
Area of path = Area of outer square − Area of inner square
17 = (8 + x)² − 64
$$\begin{gathered} \Rightarrow {\left(8+x\right)}^2=64+17=81 \\ \Rightarrow 8+x=9\Rightarrow x=1\mathrm{m} \end{gathered}$$
Thus, the width of the path is 1 m.
Hence, the correct option is (a).