Question

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.​

Answer 1

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Solution :-

Let length and breadth of rectangle be x unit and y unit.

Area = xy

According to the question,

⇒ (x - 5) (y + 3) = xy - 9

⇒ 3x - 5y - 6 = 0 ... (i)

⇒ (x + 3) (y + 2) = xy + 67

⇒ 2x - 3y – 61 = 0 ... (ii)

By cross multiplication, we get

⇒ x/305 - (-18) = y/-12 -(-183) = 1/9 - (-10)

⇒ x/323 = y/171 = 1/19

⇒ x = 17, y = 9

Length of the rectangle = 17 units.

Breadth of the rectangle = 9 units.