Question

The area of rectangle gets reduced by 50 sq. units. If its length is reduced by 5 unit and the breadth is increased by 2 unit. If we increase the length by 10 units and breadth decreased by 5 units, then the area remains same. Find the length and breadth of the rectangle.

Answer 1

Answer:

refer to the image ..

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Answer 2

Answer :

The length of the rectangle , x = 30 units

The breadth of the rectangle , y = 20 units

Given :

• The area of rectangle gets reduced by 50 sq. units. If its length is reduced by 5 unit and the breadth is increased by 2 unit. If we increase the length by 10 units and breadth decreased by 5 units, then the area remains same

To Find :

• Length and breadth of the rectangle

Solution :

Let the length of the rectangle be " x "

Breadth of the rectangle be " y "

So , Area of the rectangle = " xy "

A/c , " The area of rectangle gets reduced by 50 sq. units. If its length is reduced by 5 unit and the breadth is increased by 2 unit "

⇒ ( xy - 50 ) = ( x - 5 ) ( y + 2 )

⇒ xy - 50 = xy + 2x - 5y - 10

⇒ 2x - 5y + 40 = 0 ... (1)

A/c , " If we increase the length by 10 units and breadth decreased by 5 units, then the area remains same "

⇒ xy = ( x + 10 ) ( y - 5 )

⇒ xy = xy - 5x + 10y - 50

⇒ 5x - 10y + 50 = 0 ... (2)

Now , solve 2*(1) - (2) , we get ,

⇒ ( 4x - 10y + 80 ) - ( 5x - 10y + 50 ) = 0

⇒ - x + 30 = 0

⇒ x = 30 units

sub. x value in (2) , we get ,

⇒ 10y = 5(30) + 50

⇒ 10y = 200

⇒ y = 20 units