Question

if the length and the breadth of a rectangular park is decrease by 2m,then the area will be decrease by 196m square. if its area will be increased by 246m square if length is increased by 3m and breadth is increased by 2m. find the length and breadth of the park.

Answer 1

Let the length and breadth of the rectangular park be "x" and "y" respectively.
Given, if the length and breadth are decreased by 2m, then the area will decrease by 196 sq. metres.
i.e, (x-2)(y-2) = xy - 196 [ ∵ Area of park = xy] → (1)
Also, the area increases by 246 sq. metres if the length is increased by 3m and the breadth is increased by 2m,
∴ (x+3)(y+2) = xy + 246 → (2)
In (1), xy-2x-2y+4 = xy-196 ⇒ -2x-2y=-200 ⇒ x+y=100 → (3)
In (2), xy+2x+3y+6 = xy+246 ⇒ 2x+3y=240→ (4)
Solving Eqs. (3) and (4), we get -
x = 60m and y = 40m
Hence, Length of the park = 60m, Breadth of the park = 40m