Question

the length of rectangle is 7 less than twice it's breadth if the length is decreased by 2cm and breadth increased by 3cm the perimeter of the resulting rectangle is 66cm Find the length and the breadth of the original rectangle​

Answer 1

Answer:

Length of the rectangle = 19 m

Breadth of the rectangle = 13 m

Step-by-step explanation:

Given:

• Length of rectangle = 7 less than twice its breadth
• If length is decreased by 2 cm and breadth increased by 3 cm, the perimeter of the resulting rectangle is 66 cm.

To Find:

• Length and breadth of the original

Solution:

Let the breadth of the rectangle be x m.

By given,

Length of the rectangle =  2 (breadth) - 7 = 2x - 7 m

Now,

New length of the rectangle = 2x - 7 - 2

New length = 2x - 9  m

New breadth = x + 3 m

Now finding the perimeter of the new rectangle,

Perimeter of the rectangle is given by,

Perimeter of a rectangle = 2 (length + breadth)

Perimeter of new rectangle = 2 ( 2x - 9  + x + 3)

⇒ 2 ( 3x - 6)

⇒ 6x - 12 m

Now by given,

Perimeter of the new rectangle = 66 m

Substitute the value,

6x - 12 = 66

x - 2 = 11

x = 13

Therefore breadth of the rectangle is 13 m.

Now finding the length,

Length = 2x - 7

Length = 2 × 13 - 7 = 26 - 7

Length = 19 m

Therefore the length of the rectangle is 19 m.

Answer 2

${ \bold { \underline{\large{Question : - }}}}$

→  The length of rectangle is 7 less than twice it's breadth if the length is decreased by 2cm and breadth increased by 3cm , the perimeter of the resulting rectangle is 66cm .  Find the length and the breadth of the original rectangle .

${ \bold { \underline{\large{Answer : - }}}}$

Given : -

→ The length of rectangle is 7 less than twice it's breadth.

→ After making changes the perimeter of that rectangle becomes 66 cm

Find : -

The length and the breadth of the original rectangle in which the changes were made .

Solution : -

→ Let the breadth of the original rectangle be x cm

→ Then , length will be (2x - 7)cm

(According to the given question )

→ After the changes were made in the rectangle

The breadth will be ( x + 3 )cm

and length will be ( 2x - 7 -  2 )cm = ( 2x - 9 )cm

→ As we know that perimeter of a rectangle is 2( length + breadth )

and the perimeter of the changed rectangle is 66 cm ( given )

⇒ 66 cm = 2( length + breadth ) cm

⇒ 66 cm = 2( {2x - 9 } + {x + 3 } ) cm

⇒ 66 cm = 2( { 2x + x } + { -9 + 3 } ) cm

⇒ 66 cm = 2 ( 3x - 6 ) cm

⇒ 66 cm = 6x - 12 cm

⇒ 11 cm = x - 2

⇒ x = 11 + 2 cm

⇒ x = 13 cm

→ Now , we have to find the length and the breadth of the original rectangle

length of original rectangle = ( 2x - 7 ) cm

⇒ ( 2 × 13 - 7 ) cm

⇒ ( 26 - 7 ) cm = 19 cm

Breadth of the original rectangle = x

⇒ x = 13 cm

_______________