Question

The area of a rectangle gets reduced by 9 square units, if its length is
reduced by 5 units and the breadth is increased by 3 units. The area is
increased by 67 square units if length is increased by 3 units and breadth is
increased by 2 units. Find the perimeter of the rectangle. [CBSE 2012]​

Answer 1

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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

${\fboxed{ x = 17, y = 9}}$

Length of the rectangle = 17 units.

Breadth of the rectangle = 9 units.

Answer 2

Let, the length and breadth of the rectangle be “ x ” & “ y ” units respectively. Then,

⟹ Area = sq. units

✒ If length is reduced by 5 units and the breadth is increases by 3 units, then area is reduced by 9 square units.

➡ xy - 9 = (x - 5)(y + 3)

➡ xy - 9 = xy + 3x - 5y - 15

➡ 3x - 5y - 6 = 0 ....... (1)

✒ When length is increased by 3 units and breadth by 2 units, the area is increased by 67 sq. units.

➡ xy + 67 = (x + 3)(y + 2)

➡ xy + 67 = xy + 2x + 3y + 6

➡ 2x + 3y - 61 = 0 ....... (2)

✒ From the equations (1) & (2), by using cross multiplication, we get

➡ [ x/(305 + 18) ] = [ -y/(- 183 + 12) ] = 1/19

➡ x = 323/19

➡ x = 17

➡ y = 171/19

➡ y = 19

Hence, the length and breadth of the rectangle are 17 units and 19 units respectively.

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Step-by-step explanation:

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