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 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 : Correct Answer 5 m

Let the width of the path be x
Then,
$$\left$$       $$ = 600$$
$$\eqalign{ & \Rightarrow \left \cr & \Rightarrow 4{x^2} - 140x + 600 = 0 \cr & \Rightarrow {x^2} - 35x + 150 = 0 \cr & \Rightarrow {x^2} - 30x - 5x + 150 = 0 \cr & \Rightarrow \left( {x - 30} \right)\left( {x - 5} \right) = 0 \cr & \Rightarrow x = 5\,m\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left \cr} $$
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