In a rectangle if length is increased and breadth is reduced by $2$ metre, the area is reduced by $28 s q . m .$ If length is reduced by $1$ metre and breadth is increased by $2$ metre, the area increased by $33 s q . m .$ Find the length and breadth of rectangle.

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Solution

Let x = length & breadth = y
Area = $x . y = A$
(i) $(x + 2) (y - 2) = (A - 26) \Rightarrow x y - 2 x + 2 y - 4 = x y - 28 \Rightarrow y - x = - 12$ ...(1)
(ii) $(x - 1) (y + 2) = A + 33 \Rightarrow x y + 2 x - y - 2 = x y + 33 \Rightarrow 2 x - y = 35$ ...(2)
adding both equation
$x = 23, y - x + 2 x - y = - 12 + 35 \Rightarrow x = 23$
Placing in equation (1)
$y - 23 = - 12 \Rightarrow y = 11$

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In a rectangle if length is increased and breadth is reduced by 2 metre, the area is reduced by 28sq.m. If length is reduced by 1 metre and breadth is increased by 2 metre, the area increased by 33sq.m.Find the length and breadth of rectangle.

Let x = length & breadth = y Area = x.y=A(i) (x+2)(y−2)=(A−26)⇒xy−2x+2y−4=xy−28⇒y−x=−12 ...(1)(ii) (x−1)(y+2)=A+33⇒xy+2x−y−2=xy+33⇒2x−y=35 ...(2)adding both equationx=23,y−x+2x−y=−12+35⇒x=23Placing in equation (1)y−23=−12⇒y=11

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