A path of uniform width runs round the inside of a rectangular field…

Question

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 :

Accepted Answer

Option A. 5 m. Answer & Solution Answer: Option A Solution: Let the width of the path be x Then, [ ( 38 × 32 ) - \ ( 38 - 2x ) ( 32 - 2x ) \ ] = 600 & [ 1216 - ( 1216 - 140x + 4x^2 ) ] & 4x^2 - 140x + 600 = 0 & x^2 - 35x + 150 = 0 & x^2 - 30x - 5x + 150 = 0 & ( x - 30 ) ( x - 5 ) = 0 & x = 5\,…