Question

The area of a rectangle gets reduced by 10 square units. If its length is reduced by 4 units, the area is increased by 96 square units. Find the length and breadth of the rectangle. Please help !!

Answer 1

$\bigstar$ Correct Question :

The area of a rectangle gets reduced by 10 square units if its length is reduced by 4 units and breadth is increase by 2 units. If we increased the length by 3 units and breadth by 4 units, the area is increased by 96 square units. Find the length and breadth of the rectangle. ​

$\bigstar$ Answer :

Let the length & breadth of the rectangle be " x " & " y "

A/c , " The area of a rectangle gets reduced by 10 square units if its length is reduced by 4 units and breadth is increase by 2 units "

Area of the rectangle = xy

⇒ ( xy - 10 ) = ( x - 4 ) ( y + 2 )

⇒ xy - 10 = xy + 2x - 4y - 8

⇒ 2x - 4y + 2 = 0

⇒ 4y - 2x = 2

⇒ 2y - x = 1 ... (1)

A/c , " If we increased the length by 3 units and breadth by 4 units, the area is increased by 96 square units "

⇒ ( x + 3 ) ( y + 4 ) = ( xy + 96 )

⇒ xy + 4x + 3y + 12 = xy + 96

⇒ 4x + 3y = 84 ... (2)

Now add (2) & 4 (1) , we get ,

⇒ 4x + 3y + 8y - 4x = 84 + 4

⇒ 11y = 88

⇒ y = 8

sub. y value in (1) , we get ,

⇒ x = 2(8) - 1

⇒ x = 15

So , the Length of the rectangle = x = 15 units

Breadth of the rectangle = y = 8 units