Question

If the length of a rectangle is decreased by 5 units and its breadth increased by2
units then the area of the rectangle decreases by 80 square units. If its length is
increased by 10 units and its breadth decreased by 5 units then the area of the
rectangle increases by 50 square units. Find the original length and breadth of the
rectangle
​

Answer 1

Answer:

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.

(-)....(+).....(-)

________________

y=30

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

=> 2 × 30 - x = 20.

=> 60 - x = 20.

=> x = 60 - 20.

x=40

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

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