Q. 44.3( 6 Votes )

A rectangular fie

Answer :

Length of the rectangular field = 20m


Breadth of the rectangular field = 14m


Let x be the uniform width all around the path.


Length of the rectangular field including the path


= 20 + x + x


= 20 + 2x


Width of the rectangular field including path


= 14 + x + x


= 14 + 2x


Area of path = area of rectangular field including path – area of rectangular field


111 = (20 + 2x)(14 + 2x) – (20 × 14)


111 = 280 + 40x + 28x + 4x2 – 280


111 = 68x + 4x2


4x2 + 68x – 111 = 0


4x2 + 74x – 6x – 111 = 0


2x(2x + 37) – 3(2x + 37) = 0


(2x + 37)(2x – 3) = 0


2x + 37 = 0 or 2x – 3 = 0


2x = –37 or 2x = 3



x = –18.5 or x = 1.5


Therefore, width of the path = 1.5m


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