in the length of a rectangle is decreased by 5 units and its breadth increase by 2 units then the area of the rectangle decreases by 80 square units. if its length is increased by 10 units and its breadth decreases by 5 units then the area of the rectangle increase by 50 square units. find the original length and width of the rectangle
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Answer:
Step-by-step explanation:
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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.
(-)....(+).....(-)
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putting the value of ‘y’ in equation (2).
=> 2 × 30 - x = 20.
=> 60 - x = 20.
=> x = 60 - 20.
✔✔ Hence, Length = 40 units and breadth = 30 units. ✅✅
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