The dimension of a rectangular court is such that if the length were increased by $2$ metres and the breadth diminished by the same, its area would be diminished by $12$ square metres, and if the length were increased by $2$ metres and its breadth increased by the same. Its area would be increased by $44$ square metres. Find the length.

10 m

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13 m

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12 m

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14 m

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Solution

The correct option is C $12 m$
Let the length be $x$ and breadth be $y$
Then area $= x y$
As per the given statements, $(x + 2) (y - 2) = x y - 12$
$=> x y - 2 x + 2 y - 4 = x y - 12$
$- 2 x + 2 y = - 8$
$x - y = 4$ -- (1)
Also given, $(x + 2) (y + 2) = x y + 44$
$=> x y + 2 x + 2 y + 4 = x y + 44$
$2 x + 2 y = 40$
$x + y = 20$ -- (1)
Adding equations $5$ and $6$ , we get $2 x = 24 => x = 12$
Hence the length is $12 m .$

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