Question

the breadth of rectangle is 8cm less than its length if the length is incresed by 4cm and the breadth is incresed by 9cm the area of rectangle is found to increase by 147 sq cm find the length and breadth of rectangle plse slove this question my exam is coming soon​

Answer 1

Answer:

see photo for your answer

Answer 2

Answer:

$\large{\underline{\boxed{\sf Length = 11 \: cm}}}$

$\large{\underline{\boxed{\sf Breadth = 3 \: cm}}}$

Step-by-step explanation:

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

$\rule{300}{2}$

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 = $\sf \dfrac{143}{13}$

⇒ x = 11

Now,

Length of rectangle = x = 11 cm

Breadth of rectangle = x - 8

                                   = 3 cm

$\rule{300}{2}$

∴ The length of the rectangle is 11 cm and breadth of the rectangle is 3 cm respectively.