Question

A rectangle has an area of 315 cm² . If the length is increased by 2 cm and the width is

decreased by 2 cm, the area would decrease by 21 cm² Find the dimensions of the original
rectangle (Round your answer to 3 significant figures where necessary.)​

Answer 1

Let the breadth be x and the length be y .

Original area =x.y

Now

length=y+2

breadth=x-2

Area=x.y-28 or x-2 × y+2

xy-28=(x-2)(y+2)

xy-28=xy+2x-2y-4

2y-2x=24

y-x=12

y=12+x

length=y-1

breadth=x+2

Area=xy+33 or (x+2)(y-1)

xy+33=(x+2)(y-1)

xy+33=xy-x+2y-2

35=2y-x

2y=35+x

y=(35+x)÷2

12+x=(35+x)÷2

24+2x=35+x

x=35-24

x=11

y=23

Therefore length is 23cm and breadth is 11cm