A rectangular field is 16m long and 10m wide . There is a path of uniform width all around it having an area of 120msquare. Form the quadratic equation .
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Let width of the path be xm.

Area of the outer rectangle
= (16 + 2x) (10 + 2x)
= 160 + 32x + 20x + 4x2
= 160 + 52x + 4x2
Area of the inner rectangle
= 16m X 10m
= 160m2
Area of the path
= 160 + 52x + 4x2 - 160 = 120
or, 4x2 + 52x - 120 = 0
or, x2 + 13x - 30 = 0
or, (x + 15) (x - 2) = 0
or, x = -15, 2
As width can not be negative  x = 2 m
i. e. width of the path = 2 m
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Area of the outer rectangle
= (16 + 2x) (10 + 2x)
= 160 + 32x + 20x + 4x2
= 160 + 52x + 4x2
Area of the inner rectangle
= 16m X 10m
= 160m2
Area of the path
= 160 + 52x + 4x2 - 160 = 120
or, 4x2 + 52x - 120 = 0
or, x2 + 13x - 30 = 0
or, (x + 15) (x - 2) = 0
or, x = -15, 2
As width can not be negative  x = 2 m
i. e. width of the path = 2 m
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