When both the length and the breadth of a rectangle are tripled, the area will increase by a factor of 9.

Here’s why:

• The area $A$ of a rectangle is calculated as: $A = \text{length} \times \text{breadth}$

• Let the original length be $L$ and the original breadth be $B$. So, the original area is: $A_{\text{original}} = L \times B$

• If both the length and breadth are tripled, the new length becomes $3L$ and the new breadth becomes $3B$. The new area $A_{\text{new}}$ is: $A_{\text{new}} = (3L) \times (3B) = 9 \times (L \times B)$

Thus, the new area is 9 times the original area.

Do you need more details or have any questions?

Here are 5 related questions:

1. How will the area change if only the length is doubled but the breadth remains the same?
2. If the area of a rectangle is given, can you find the new area after scaling both dimensions by 4?
3. What happens to the perimeter if both the length and breadth are tripled?
4. How does increasing one dimension affect the area compared to increasing both dimensions?
5. Can you explain how to calculate the area of other shapes, like triangles or circles?

Tip: When both dimensions of a shape are scaled by a factor, the area changes by the square of that factor.