Question

(iii) A rectangle has the same area as another, whose length is 6 m more and breadth
is 4 m less. It has also the same area as the third, whose length is 8 m more and
breadth 5 m less. Find the length and breadth of the original rectangle.​

Answer 1

Let the length of original rectangle be l and breadth of original rectangle be b

Area of the original rectangle is lb

Case 1 :

Length of second rectangle is ( l + 6)

Breadth of second rectangle is ( b - 4)

Area of this rectangle = (l+6)(b-4) = lb + 6b - 4l - 24

Area of original rectangle = Area of second rectangle.

⇒ lb = lb + 6b - 4l - 24

⇒ 6b - 4l = 24 .... ( Equation 1)

Case 2 :

Length of third rectangle is ( l + 8)

Breadth of second rectangle is ( b - 5)

Area of this rectangle = (l+8)(b-5) = lb + 8b - 5l - 40

Area of original rectangle = Area of third rectangle.

⇒ lb = lb + 8b - 5l - 40

⇒ 8b - 5l = 40 .... ( Equation 2)

(1)× 5 ⇒ 30 b - 20 l = 120

(2) × 4 ⇒ 32b - 20l = 160

Subtracting them gives,

⇒ 2b = 40

⇒ b = 20

⇒ 8(20) - 5l = 40

⇒ 5l = 120

⇒ l = 24

Therefore, The Area of the original rectangle is 24 × 20 = 480 m²

Answer 2

Answer:

Length = 24 m and Breadth = 20 m of the Original rectangle

Step-by-step explanation:

We Have :-

3 Rectangles

A rectangle has the same area as another, whose length is 6 m more and breadth is 4 m less.

It has also the same area as the third, whose length is 8 m more and breadth 5 m less

To Find :-

Length and Breadth of Original Rectangle

Formula Used :-

Area of Rectangle = Length * Breadth

Solution :-

First Rectangle , let the

Length = x

Breadth = y

Second Rectangle , let the

Length = x + 6

Breadth = y - 4

Third Rectangle , let the

Length = x + 8

Breadth = y - 5

Area 1 = Area 2 = Area 3

Taking Area 1 = Area 2

x y = ( x + 6 ) ( y - 4 )

x y = x y - 4x + 6y - 24

6y - 4x = 24

3x - 2y = 12

x = ( 3y - 12 ) / 2 ------------ ( i )

Taking Area 2 = Area 3

( x + 6 ) ( y - 4 ) = ( x + 8 ) ( y - 5 )

x y - 4x + 6y - 24 = x y - 5x + 8y - 40

x - 2y = - 16

( 3y - 12 ) / 2 - 2y = - 16    ( Using i )

3y - 12 - 4y = -32

- 12 - y = - 32

12 + y = 32

y = 20 ------------- ( ii )

Putting in ( i )

x = ( 3y - 12 ) / 2

x = 24

Length = 24 m and Breadth = 20 m of the Original Rectangle