Question

$DDA$ wants to make a rectangular park in the colony. If the length and breadth of the park is decreased by $2m$, then the area will be decreed by $196$ square meters. Its area will be increased by $246$ square meters if its length is increased by $3m$ and breadth is increased by $2m$. Find the length and breadth of the park.

Answer 1

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Let $x$ and $y$ be the length and breadth of the given rectangle.

From the question$\left(1\right)\Rightarrow (x-2)(y-2)=xy-196$

$\Rightarrow -2x-2y=-200$ ........$\left(1\right)$

$(x+3)(y+2)=xy+246$

$\Rightarrow xy+2x+3y+6=xy+246$

$\Rightarrow 2x+3y=240$ ...........$\left(2\right)$

Adding $\left(1\right)$ and $\left(2\right)$ we get

$y=40$

Eqn$\left(2\right)\Rightarrow 2x=120$

$\therefore x=60$

$\therefore$ Length $=60$ m and Breadth $=40$ m

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