Answer:

● PERIMETER of rectangle is 52 units.

Step-by-step explanation:

Let ,

length and breadth of Rectangle be l and b respectively.

then, area of rectangle will be l b

First case :

when length is reduced by 5 units and breadth is INCREASED by 3 units then, area of rectangle is reduced by 9 sq. units.

so,

→ ( l - 5 ) ( b + 3 ) = l b - 9

→ l b + 3 l - 5 b - 15 = l b - 9

→ 3 l - 5 b - 15 = - 9

→ 3 l - 5 b = 6

→ 3 l = 6 + 5 b

→ l = ( 6 + 5 b ) / 3  ____eqn①

Second case :

when length is increased by 3 units and breadth is increased by 2 units then area of rectangle is increased by 67 sq. units.

so,

→ ( l + 3 ) ( b + 2 ) = l b + 67

→ l b + 2 l + 3 b + 6 = l b + 67

→ 2 l + 3 b = 67 - 6

→ 2 l + 3 b = 61

[ using equation ① ]

→ 2 ((6+5b)/3) + 3 b = 61

→ (12 + 10 b)/3 + 3 b = 61

[ multiplying by 3 both sides ]

→ 12 + 10 b + 9 b = 183

→ 19 b = 183 - 12

→ 19 b = 171

→ b = 171 / 19

→ b = 9 units

[ putting VALUE of b in eqn ① ]

→ l = ( 6 + 5 b ) / 3

→ l = ( 6 + 5 (9) ) / 3

→ l = 51 / 3

→ l = 17 units

Therefore,

Length and breadth of rectangle are 8 units and 17 units respectively.

so,

→ perimeter of rectangle = 2 ( l + b )

→ perimeter of rectangle = 2 ( 9 + 17 )

→ perimeter of rectangle = 52 units.

Therefore,

perimeter of rectangle is 52 units.