1.

a rectangular field is 16 metre long and 10 M broad there is a path of equal with all around inside it if the area of the path is 120 square find the width of the path​

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Answer:

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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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