Q. 84.0( 40 Votes )

# If the length of a rectangle is reduced by 5 units and its breadth is increased by 3 units, then the area of the rectangle is reduced by 8 square units. If length is reduced by 3 units and breadth is increased by 2 units, then the area of rectangle will increase by 67 square units. Then find the length and breadth of the rectangle.

Answer :

Let the length be 'x' and breadth be 'y'

Area of rectangle = length × breadth

Area of rectangle = xy

First case:

Length = x - 5

Breadth = y + 3

As, area is reduced by 8 sq. units

⇒ xy - (x - 5)(y + 3) = 8

⇒ xy - (xy + 3x - 5y - 15) = 8

⇒ xy - xy - 3x + 5y + 15 = 8

⇒ 3x - 5y = 7 eq.[1]

Second case:

Length = x - 3

Breadth = y + 2

As, the area is increased by 67 units

⇒ (x - 3)(y + 2) - xy = 67

⇒ xy + 2x - 3y - 6 - xy = 67

⇒ 2x - 3y = 73 eq.[2]

Multiplying eq.[1] by 2 both side, and Multiplying eq.[2] by 3 both side, we get

⇒ 6x - 10y = 14 eq.[3]

⇒ 6x - 9y = 219 eq.[4]

Subtracting eq.[3] from eq.[4]

⇒ 6x - 9y - 6x + 10y = 219 - 14

⇒ y = 205

Using this in eq.[1]

⇒ 3x - 5(205) = 7

⇒ 3x - 1025 = 7

⇒ 3x = 1032

⇒ x = 344

Hence, length = x = 344 units

Breadth = y = 219 units.

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