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Let the length of the rectangle be x units and the breadth be y units
Area of the rectangle=length×breadth
=x×y=xy sq. units
From the given information, we have,
(x+2)×(y−2)=xy−28
and(x−1)×(y+2)=xy+33
(x+2)×(y−2)=xy−28
⇒xy−2x+2y−4=xy−28
⇒−2x+2y=−24
⇒−x+y=−12
⇒x=y+12....(i)
Also,(x−1)×(y+2)=xy+33
⇒xy+2x−y−2=xy+33
⇒2x−y=35....(ii)
Substituting equation (i) in equation (ii), we get,
2x−y=35
⇒2(y+12)−y=35
⇒2y+24−y=35
⇒y=11
Substituting y=11 in equation (i), we get,
x=y+12
⇒x=11+12
⇒x=23
Therefore, length of rectangle =x=23 units
and breadth of rectangle =y=11 units
Area of rectangle =xy=23×11=253 square units
Hope it helps!!!
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