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1. A path of uniform width runs round the inside of a rectangular field 38 m long 32 m wide. If the path occupies 600 m², then the width of the path is :

A. 5 m

B. 10 m

C. 18.75 m

D. 30 m

Solution:

Let the width of the path be x
Then,

[(38 \times 32) - {(38 - 2 x) (32 - 2 x)}]

= 600

\begin{aligned} \Rightarrow [1216 - (1216 - 140 x + 4 x^{2})] \\ \Rightarrow 4 x^{2} - 140 x + 600 = 0 \\ \Rightarrow x^{2} - 35 x + 150 = 0 \\ \Rightarrow x^{2} - 30 x - 5 x + 150 = 0 \\ \Rightarrow (x - 30) (x - 5) = 0 \\ \Rightarrow x = 5 m [∴ x \neq 30] \end{aligned}

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