Question

The ratio of length and breadth of a rectangle is 3:2. If its area is 2400 square cm, then what is its perimeter (in cms)?

• A. 180
• B. 220
• C. 200
• D. 240

Answer 1

The Correct Option is C

Rectangle Area and Perimeter Calculation 

Step 1: Define the Length and Breadth of the Rectangle

Let the length of the rectangle be 3x and the breadth be 2x, where x is a constant.

Step 2: Calculate the Area of the Rectangle

The area of the rectangle is given as:

\[ \text{Area} = \text{Length} \times \text{Breadth} = 3x \times 2x = 6x^2 \]

We are told that the area is 2400 square cm, so:

\[ 6x^2 = 2400 \]

Step 3: Solve for x

\[ x^2 = \frac{2400}{6} = 400 \] \[ x = \sqrt{400} = 20 \]

Step 4: Calculate the Length and Breadth

• Length = 3x = 3 × 20 = 60 cm
• Breadth = 2x = 2 × 20 = 40 cm

Step 5: Calculate the Perimeter of the Rectangle

The perimeter of the rectangle is given by:

\[ \text{Perimeter} = 2 \times (\text{Length} + \text{Breadth}) = 2 \times (60 + 40) = 2 \times 100 = 200 \, \text{cm} \]

Final Answer:

The perimeter of the rectangle is 200 cm.

Conclusion:

The correct answer is (c) 200.