A path of uniform width turns the inside of a rectangular field 38m long and 32

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Question

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

Options:

A . 3m

B . 5m

C . 8.75m

D . 10m

Answer: Option B

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+4x² -140x
Area of the path = 1216 “(1216 +4x2 -140x)
= 140x -4x²
140x -4x² = 600
=> 4x²-140x +600 =0
=> x² -35x +150 =0
=> (x-30)(x-5)=0
=> X =5 m

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