In a rectangle,if the length is increased by 5 units and breadth is decreased by 3 unit, the area decreased by 5 square unit .If the length is increased by 3 unit and breadth is increased by 2 units ,the area is increased by 50 square units.Find the length and breadth of the rectangle.
Answers
Step-by-step explanation:
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
Answered By
toppr
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