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Solution


Q.

The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.

Ans.

(9)

Let length and breadth be x and y , Area = xy

1st condition: ( x – 5 ) ( y + 3 ) = xy – 9

⇒ 3x – 5y = 6

2nd condition: ( x + 3 ) ( y + 2 ) = xy + 67

⇒ 2x + 3y = 61

Solve 1st and 2nd equations, we get x = 17 and y = 9

Hence, Length of rectangle = 17 units and breadth of rectangle = 9 units