Question

If in a rectangle, the length is increased and breadth is reduced each by 2 units, the area is reduced by 28 sq. units. if however , the length is reduced by 1 unit and breadth is increased by 2 units, the area increases by 33 square units. Find the area of rectangle .​

Answer 1

Answer:

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