Final answer:
The scale factor relating the areas of similar figures is the square of the linear scale factor. Therefore, if the scale factor is 2, the area would scale up by a factor of 4, which matches the given option of k=2.
Step-by-step explanation:
The student has asked about the scale factor for the area of similar figures. If triangle R has an area of 40 square units and Salome drew a scaled version of it, labeled triangle T, then the scaling involves understanding how areas scale. Since the question is asking for which scale value, labeled as k, corresponds to an increase in area, we need to remember that the area of similar figures scales by the square of the scale factor for their corresponding sides. This means if the scale factor of the lengths is k, then the scale factor for the area is k2.
In this case, since there aren't any specific areas provided for triangle T, and no specific relationship between the areas of triangle R and T is given, we cannot determine the exact value of k without more information. However, from the statement that 'The area of the larger square is 4 times larger than the area of the smaller square,' we can infer that if k was 2, then the area would indeed be 4 times larger (since 22 = 4). This leads us to conclude that the scale factor (k) is 2, option c).