Question

The breadth of a rectangle is 8 cm less
than its length. If the length is increased
by 4 cm and the breadth is increased by
9 cm, the area of the rectangle is increased
by 147 cm2. Find the length and breadth
of the rectangle.


please answer this question ​

Answer 1

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

Answer 2

${\huge{\underline{\underline{\sf{\blue{Solution :-}}}}}}$

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

$∴ \: \: \: \: \: \: \: x \: = \frac{143}{13} = 11 \: cm$

( 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

${\huge{\underline{\underline{\sf{\blue{ATQ:-}}}}}}$

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

$= > x ^{2} - 8x \: + 147 \: = x ^{2} \: + x + 4x + 4$

$= > 147 - 4 = 5x + 8x$

$= > 143 = 13x$

$= > \: Thus , \: length \: = 11 \: cm \: and \: </p><p>breadth \: = ( 11 - 8 ) = 3 cm$