The length and breadth of a rectangle are in the ratio 3 : 2. If the length is increased by 5 m keeping the breadth same, the new area of rectangle is 2600 m². What is the perimeter of the original rectangle?

Given:

Length : breadth = 3 : 2

Length is increased by 5 m keeping the breadth same

New area become 2600 m2

Formula used:

Area of rectangle = Length × breadth 

Perimeter = 2 (Length + breadth)

Calculation:

Let length & breadth be '3y' & '2y' respectively.

According to the question

⇒ (3y + 5) × 2y = 2600

⇒ 6y² + 10y = 2600 

⇒ 6y² + 10y - 2600 = 0

⇒ 3y² + 5y - 1300 = 0

⇒ 3y² - 60y + 65y - 1300 = 0

⇒ 3y(y - 20) + 65(y - 20) = 0

⇒ (3y + 65)(y - 20) = 0

⇒  y = 20, y ≠ - (65/3)

Since, length can not be negative.

Therefore, length & breadth of original rectangle

3y = 3 × 20 = 60

2y = 2 × 20 = 40

Hence, perimeter = 2(60 + 40) = 200

∴ Perimeter of the rectangle is 200 m.