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.
Answers
Answer:
Step-by-step explanation:
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.
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