Question

the length of rectangle is 5cm more than its breadth. If the length is increased by 6cm and breadth is decreased by 3cm, then the new perimeter become 8/7 of the original perimeter. find the length and the breadth of the original rectangle.

Answer 1

Answer:

Length of the original rectangle is 13 cm and breadth is 8 cm.

Step-by-step explanation:

Let the breadth of the rectangle be a cm ,

[ As length is 5 cm more than the breadth ]

Let the length of the rectangle be ( a + 5 ) cm

Now,

Length of the rectangle = ( a + 5 ) cm

Breadth of the rectangle = a cm

[ Perimeter of rectangle = 2( length + breadth ) ]

Perimeter of the original rectangle = 2[ a cm + ( a + 5 ) cm ]

Perimeter of the original rectangle = 2[ a + a + 5 ] cm

Perimeter of the original rectangle = 2( 2a + 5 ) cm

According to the question : -

If the length is increased by 6cm and breadth is decreased by 3cm, then the new perimeter become 8/7 of the original perimeter.

Now,

Length of the rectangle = 6 cm + ( a + 5 ) cm

Length of the rectangle = 6 + 5 + a cm

Length of the rectangle = ( a + 11 ) cm

And,

Breadth of the rectangle = a cm - 3 cm

Breadth of the rectangle = ( a - 3 ) cm

Therefore,

New perimeter of the rectangle = [ ( a + 11 ) cm + ( a - 3 ) cm ]

New perimeter = 2( a + 11 + a - 3 ) cm

New perimeter = 2( 2a + 8 ) cm

Given that the new perimeter becomes 8 / 7 of the original perimeter.

So,

⇒ New perimeter = 8 / 7 of old perimeter

= >  2( 2a + 8 ) = 8 / 7 x 2( 2a + 5 )

= >  ( 2a + 8 ) = 8 / 7 x ( 2a + 5 )

= >  7( 2a + 8 ) = 8 x ( 2a + 5 )

= >  14a + 56 = 16a + 40

= >  56 - 40 = 16a - 14a

=  >  16 = 2a

= >  8 = a

Then,

Length of the original rectangle = ( a + 5 ) cm = ( 8 + 5 ) cm = 13 cm

Breadth of the original rectangle = a = 8 cm

Answer 2

Answer:

Length = 13 cm

Breadth = 8 cm

Step-by-step explanation:

Let the length of the rectangle be 'x' and breadth of the rectangle be 'y'.

Given that Length of rectangle is 5 cm more than its breadth.

Hence, Length(x) = y + 5   ----- (*)

Perimeter of rectangle = 2(l + b).

                                      = 2(y + 5 + y)

                                      = 2(2y + 5)

                                      = 4y + 10.

Hence, original Perimeter = 4y + 10.

(i)

Length is increased by 6 cm and breadth is decreased by 3 cm.

Length = y + 5 + 6

Breadth = y - 3.

Perimeter = 2(y + 5 + 6 + y - 3)

                = 2(2y + 8)

                = 4y + 16

Now,

Given that New perimeter become 8/7 of the original perimeter.

(4y + 16) = 8/7(4y + 10)

7(4y + 16) = 8(4y + 10)

28y + 112 = 32y + 80

4y = 32

y = 8.

Substitute y = 8 in (*), we get

=> x = y + 5

=> x = 8 + 5

=> x = 13

Therefore:

Length of the original rectangle = 13 cm

Breadth of the original rectangle = 8 cm

Hope it helps!