If both the length and breadth of a rectangle are tripled, the area of the rectangle will increase by a factor of $3 \times 3 = 9$.

Explanation:

Let the original length of the rectangle be $L$ and the breadth be $B$. The area of the rectangle is given by:

$\text{Original Area} = L \times B$

When both the length and breadth are tripled, the new length is $3L$ and the new breadth is $3B$. The new area is:

$\text{New Area} = 3L \times 3B = 9 \times (L \times B)$

Thus, the area becomes 9 times larger.

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Would you like more details or have any questions? Here are some related questions:

1. What happens to the area if the length is doubled but the breadth remains the same?
2. How does the perimeter of the rectangle change when both length and breadth are tripled?
3. What would happen to the area if only the length were tripled but the breadth remained the same?
4. How do changes in dimensions affect the diagonal of a rectangle?
5. Can the same reasoning be applied to other shapes, like squares or triangles?

Tip: In general, when scaling dimensions of a 2D shape, the area scales by the square of the scale factor.