Final answer:
Tripling both the length and width of a rectangle multiplies the original area by nine. For a rectangle with an original area of 40 m², the new area would be 360 m² after tripling both dimensions.
Step-by-step explanation:
The area of a rectangle is given by the product of its length and width. If both the length and width of a rectangle are tripled, the new area is nine times the original area because the scale factor for both dimensions is three, and area is a two-dimensional measurement (length × width). Hence, if the original area is 40 m², the area of the new rectangle will be 40 m² × 3 × 3, which equals 360 m².
To illustrate this concept using a square as an example, if Marta has a square with a side length of 4 inches, and she creates a new square with dimensions twice that of the original, the side length of the new square would be 8 inches (4 inches × 2). Therefore, the area of the larger square would be 8 inches × 8 inches, giving an area of 64 square inches, which is four times the area of the smaller square (4 inches × 4 inches = 16 square inches). This illustrates how changes in linear dimensions affect the area by the square of the scale factor.