Let the length of the rectangle be x cm. Then, it's breadth = (x - 8) cm.

Area of rectangle = x(x - 8) cm²

If the length is increased by 4 cm and breadth is increased by 9 cm, area of rectangle is increased by 147 sq cm.

Increased length = (x + 4) cm

Increased breadth = (x - 8 + 9) cm

                               = (x + 1) cm

Increased area = (x² - 8x + 147) cm²

Area of rectangle = Length * Breadth

⇒ x² - 8x + 147 = (x + 4)(x + 1)

⇒ x² - 8x + 147 = x² + 4x + x + 4

⇒ x² - 8x + 147 = x² + 5x + 4

⇒ x² - 8x + 147 - x² - 5x - 4 = 0

⇒ - 13x + 143 = 0

⇒ - 13x = - 143

⇒ x = \sf \dfrac{143}{13}13143

⇒ x = 11

Now,

Length of rectangle = x = 11 cm

Breadth of rectangle = x - 8

                                   = 3 cm

Let the length of the rectangle be x cm.

Then breadth of the rectangle be ( x - 8 ) cm.

Area of the rectangle = x ( x - 8 ) cm^2

( A = l × b )

By increasing 4 cm in length and 9 cm in breadth , new length = ( x + 4) cm and new breadth = ( x - 8 + 9 ) = ( x + 1) cm

Therefore , new area = ( x + 4 ) ( x + 1 ) cm^2

x ( x - 8 ) + 147 = ( x + 4) ( x + 1)