Question

The difference between the length and breadth of a rectangle is 20 m. It's perimeter is 200 m, then what is the area?

• A. 2000 sqm
• B. 2200 sqm
• C. 2400 sqm
• D. 2600 sqm

Hint:

When you are given the sum and difference of two numbers (in this case, L+B=100 and L-B=20), you can find the numbers quickly:

Larger number (L) = (Sum + Difference) / 2 = (100 + 20) / 2 = 60.
Smaller number (B) = (Sum - Difference) / 2 = (100 - 20) / 2 = 40.

Answer 1

The Correct Option is C

Step 1: Understanding the Given Information
We are given the following for a rectangle:


Difference between length (L) and breadth (B): \( L - B = 20 \) m.
Perimeter (P) = 200 m.
We need to find the area.

Step 2: Key Formula or Approach


Perimeter of a rectangle: \( P = 2(L + B) \).
Area of a rectangle: \( A = L \times B \).
We have a system of two linear equations with two variables (L and B), which we need to solve.

Step 3: Detailed Explanation
1. Formulate the equations:
Equation (1): \( L - B = 20 \)
From the perimeter formula: \( 200 = 2(L + B) \), which simplifies to:
Equation (2): \( L + B = 100 \)
2. Solve the system of equations:
We can solve this by adding the two equations together.
\[ (L - B) + (L + B) = 20 + 100 \] \[ 2L = 120 \] \[ L = \frac{120}{2} = 60 \text{ m} \] Now substitute the value of L back into Equation (2):
\[ 60 + B = 100 \] \[ B = 100 - 60 = 40 \text{ m} \] 3. Calculate the Area:
\[ A = L \times B = 60 \text{ m} \times 40 \text{ m} = 2400 \text{ sqm} \]
Step 4: Final Answer
The area of the rectangle is 2400 square meters. Therefore, option (C) is the correct answer.