Question

If the length of a rectangle is reduced by 5 units and its breadth is increased by 2 units then
the area is reduced by 80 sq. units. However if the length is increased by 10 units and breadth
is decreased by 5 units its area increases to 50 sq. units. Find the length and breadth of the
rectangle.​

Answer 1

Answer:

• Length = 40
• Breadth = 30

Step-by-step explanation:

Given: As in first case

• Area of rectangle gets reduced by 80 sq units
• Its Length and Breadth reduced by 5 sq units and increased by 2 sq units respectively

★In second case

• Its length is increased by 10 sq units and Breadth is decreased by 5 sq units.
• Then, Area of rectangle will increase by 50 sq units.

To find:

Length and Breadth of rectangle

Solution: 

Let Length be 'x' and Breadth be 'y'.

Then, Area of rectangle will be Length x Breadth = xy

According to the question : In Case (1)

⟹ ( x–5)(y+2)=xy – 80

⟹ x(y+2) –5(y+2) = xy –80

⟹ xy + 2x – 5y –10 = xy –80

⟹ 2x – 5y –10 = –80

⟹ 2x – 5y = –80 + 10

⟹ 2x – 5y = –70 .................. ( equation 1)

→ In second case

⟹ (x+10)(y–5) = xy + 50

⟹ x(y–5) +10(y–5) = xy + 50

⟹ xy –5x + 10y –50 = xy + 50

⟹ –5x + 10y = 50 + 50

⟹ –5x + 10y = 100 ................. ( equation 2)

Now, Multiplying both sides of equation 1 by 2

=> 2(2x–5y) = 2(–70)

=> 4x – 10y = –140

Solving both equations ( eqn 1 and eqn 2)

=> –5x + 10y = 100

⠀⠀⠀4x – 10y = –140

__________________________

⠀⠀⠀–x = –40

or x = 40

Hence, We get Breadth of rectangle 'x' = 40 units

Now, Putting the value of 'x' in equation 2nd We got:

⟹ –5 x 40 + 10y = 100

⟹ –200 + 10y = 100

⟹ 10y = 100+200

⟹ 10y = 300

⟹ y = 30 units

Hence, We get Length of rectangle 'y' = 30 units.

Answer 2

Answer

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

area of the rectangle = xy.

new length = ( x - 5 ) units.

new breadth = ( y + 2 ) units.

new area = ( x - 5 ) ( y + 2 ) sq units.

xy - ( x - 5 ) ( y + 2 ) = 80.

xy - xy - 2x + 5y + 10 = 80.

5y - 2x = 70...........(1)

new length = ( x + 10 )

breadth = ( y - 5 )

area = ( x + 10 ) ( y - 5 )

( x + 10 ) ( y - 5 ) - xy = 50.

xy - 5x + 10y - 50 - xy = 50.

10y - 5x = 100.

2y - 5 = 20................(2).

=> 2( 2y - x = 20 ).

=> 4y - 2x = 40................(3)

(1) - (3)

y = 30.

the value of y in (2).

2 × 30 - x = 20.

60 - x = 20.

x = 60 - 20.

x = 40.