Question

If the length of rectangle is reduced by 5 units and its breadth is increased by 2 units then the area of rectangle is reduced by 80 square units. However, if we increase its length by 10 unit and decrease the breadth by 5 units, its area is increased by 50 square units find the length and breadth of the rectangle.

Answer 1

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Hey there !!

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

→ Then, area of the rectangle = xy sq units.

CASE 1.

➡ When the length is reduced by 5 units and the breadth is increased by 2 units.


Then, new length = ( x - 5 ) units.

and 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).



CASE 2.

When the length is increased by 10 units and the breadth is decreased by 5 unites.


Then, new length = ( x + 10 ) units.

and new breadth = ( y - 5 ) units.

=> new area = ( x + 10 ) ( y - 5 ) sq units.

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

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

=> 10y - 5x = 100.

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


▶ Now, multiply equation (2) by 2.

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

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


▶ Substracte equation (1) and (3), we get


5y - 2x = 70.
4y - 2x = 40.
(-)....(+).....(-)
___________


$\huge \boxed{ => y = 30. }$


putting the value of ‘y’ in equation (2).

=> 2 × 30 - x = 20.

=> 60 - x = 20.

=> x = 60 - 20.


$\huge \boxed{ => x = 40. }$



✔✔ Hence, Length = 40 units and breadth = 30 units. ✅✅

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$\huge \bf{ \# \mathbb{B}e \mathbb{B}rainly.}$

Answer 2

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.