Let’s solve the problem together.

The task is to determine the correct scale diagram of a rectangular carpet that is 6 meters long and 4 meters wide. The scale used is 1 cm represents 2 m.

Step 1: Convert the dimensions into scaled values

• Length: $6 \, \text{m} \div 2 \, \text{m/cm} = 3 \, \text{cm}$
• Width: $4 \, \text{m} \div 2 \, \text{m/cm} = 2 \, \text{cm}$

Thus, the scale diagram should have dimensions 3 cm by 2 cm.

Step 2: Identify the correct diagram

Looking at the options in the image:

• The rectangle labeled E is 3 squares (cm) long and 2 squares (cm) wide, matching the scaled dimensions of the carpet.

Answer:

The correct option is E.

Do you want me to explain the scaling process further? Here are some related questions to deepen your understanding:

1. How would the diagram change if the scale was 1 cm = 1 m?
2. What would the dimensions be if the carpet was 8 m by 6 m using the same scale?
3. Can you calculate the area of the scaled rectangle and verify it matches the scaled carpet area?
4. How would you handle irregular shapes with scaling?
5. What is the ratio of the carpet's real area to its scaled area?

Tip: Always double-check the units and scaling factor when solving scale diagram problems.