Question

The area of a rectangle gets reduced by 28 square units, if its length is increased by 2

units and breadth is reduced by 2 units. If its length is reduced by 1 unit and breadth

is increased by 2 units, the area increases by 33 square units. Find the length and

breadth of the rectangle.​

Answer 1

Step-by-step explanation:

Given:

• The area of a rectangle gets reduced by 28 square units, if its length is increased by 2

units and breadth is reduced by 2 units

• Tts length is reduced by 1 unit and breadth is increased by 2 units, the area increases by 33 square units

To Find

• Length and Breadth of the rectangle

Solution:

Let the length and breadth be x and y respectively

Area=xy

Case I:

New length=x+2

New breadth=y-2

New Area =(x+2)(y-2)=xy+2y-2x-4

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

→xy-xy+2y-2x=-28+4

→y-x=-12( Dividing 2 on both sides)

→x-y=12---(i)

Case II:

New length =x-1

New breadth=y+2

New Area=(x-1)(y+2)=xy+2x-y-2

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

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

2x-y=35---(ii)

Subtracting (i) from (ii)

2x-y=35

x-y=12

-. +. -

-----------

x=23

x-y=12

23-y=12

-y=12-23

-y=-11

y=11

Length=23 unit's

Breadtg=11 units