Let length of rectangle = x units

And width of rectangle = y units

Area of rectangle = length * width = x*y

The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units.

So

Decrease the length by 5 unit so new length = x - 5

Increase the width by 3 unit so new width = y + 3

New area is reduced by 9 units

So new area= xy – 9

Plug the value in formula length * width = area we get

(x- 5)(y + 3) = xy- 9

Xy+ 3x – 5y – 15= xy – 9

Subtract xy both side we get

3x - 5y= 6…(1)

If we increase the length by 3units and the breadth by 2 units, the area increases by 67 square units.

Increase the length by 3 unit so new length = x +3

Increase the width by 2 unit so new width = y + 2

New area is increasedby 67 units

So new area= xy + 67

Plug the value in formula length * width = area we get

(x+3)(y + 2) = xy+67

Xy+ 2x+3y+6= xy + 67

Subtract xy both side we get

2x+3y = 61…(2)*3

3x - 5y= 6…(1)*2

Cross multiply the coefficient of x we get

6x + 9 y = 183

6x -10y=12

Subtract now we get

19 y = 171

Y = 171/19 = 9

Plug this value of y in equation first we get

2x + 3* 9 = 61

2x= 61 – 27

2x = 34

X = 34/2 = 17

So length is 17 units and width is 9 units