A path of uniform width turns the inside of a rectangular field 38m long and 32m wide. IF the path occupies 600 m2 than the width of the path is_______?

A path of uniform width turns the inside of a rectangular field 38m long and 32m wide. IF the path occupies 600 m2 than the width of the path is_______?

A. 3m
B. 5m
C. 8.75m
D. 10m

Explanation:
Area of the field = (38 x 32)m2
Let the width of the path be x metres
Area with out path = (38-2x)(32-2x)m2
= 1216+4×2 -140x
Area of the path = 1216 –(1216 +4×2 -140x)
= 140x -4×2 140x -4×2 = 600
=> 4×2-140x +600 =0
=> x2 -35x +150 =0
=> (x-30)(x-5)=0
=> X =5 m

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