Question

Length of rectangle is 6cm more than its width .if its length and breadth each is decreased by 3cm,the area of New rectangle is decreased by 36sq cm. Find the original length and breadth of the original rectangle

Answer 1

Given :-

Length of rectangle is 6 cm more than its width .

If the length and breadth each is decreased by 3cm , then the area of new rectangle is decreased by 36 cm²

Required to find :-

• Original length and breadth of the rectangle ?

Solution :-

Given data :-

Length of rectangle is 6 cm more than its width .

If the length and breadth each is decreased by 3cm , then the area of new rectangle is decreased by 36 cm²

we need to find the original length and breadth of the rectangle .

So,

Let's consider the breadth of the rectangle be x cm

Length is 6cm more than the width = x + 6 cm

So,

Using the formula ;

Length x breadth = Area of the rectangle

=> ( x ) ( x + 6 )

=> x² + 6x

Similarly,

It is also mentioned that ;

If the length and breadth each is decreased by 3cm , then the area of new rectangle is decreased by 36 cm²

So,

Length of the rectangle = x + 6 - 3

=> x + 3 cm

Breadth of the rectangle = x - 3 cm

Area of the rectangle is decreased by 36 cm²

Using the formula ;

Length x Breadth = Area of the rectangle

( x + 3 ) ( x - 3 ) = x² + 6x - 36

x ( x - 3 ) + 3 ( x - 3 ) = x² + 6x - 36

x² - 3x + 3x - 9 = x² + 6x - 36

x² - 9 = x² + 6x - 36

x² get's cancelled on both sides

- 9 = + 6x - 36

- 9 + 36 = 6x

27 = 6x

6x = 27

x = 27/6

x = 4.5 cm

Hence,

Length of the rectangle = x + 6

=> 4.5 + 6

=> 10.5 cm

Breadth of the rectangle = x = 4.5 cm

Therefore,

Length of the rectangle = 10.5 cm

Breadth of the rectangle = 4.5 cm

Answer 2

Breadth = 4.5cm

Length = 4.5+6 = 10.5cm

Whole solution is given in the attachment