Question

The area of a rectangle gets increased by 10 square units, if its length is reduced by 2 units and breadth is increased by 2 units. If we increase the length by 3 units and breadth is reduced by 2 units, the area reduces by 12 square units. Find the dimensions of the rectangle.​

Answer 1

Answer:

Let the length be xm

And breadth be ym

Area=xy sq. meter

A. T. Q

(x-2)(y+2)=xy+10

xy+2x-2y-4=xy +10

2x-2y-4=10

2(x-y-2)=2X5

x-y-2=5

x-y-2-5=0

x-y-7=0

x-y=7..............(i)

(x+3)(y-2)=xy-12

xy-2x+3y-6=xy-12

-2x+3y-6=-12

-2x+3y=-12+6

-2x+3y=-6...........(ii)

Multiply (i) by2

2x-2y=14.......... (iii)

Add eq(ii) & (iii)

2x-2y=14

-2x+3y=-6

____________

y=8

Put value of y in eq (iii)

2x-2(8)=14

2x-16=14

2x=14+16

2x=30

x=15

Length=15m

Breadth =8m