Question

The breadth of a rectangle exceeds its length by 12 cm. If the length is increased by 4cm and breadth is decreased by 3cm such that the area of original rectangle and area of new rectangle remains same. Find the original length and breadth.

Answer 1

Answer:

Solution

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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

Step-by-step explanation: