Final answer:
The area of the triangle increases by a factor of 9.
Step-by-step explanation:
To find the area of a triangle, we can use the formula A = 1/2 × base × height. Given that the base is 12 units and the height is 7 units, the initial area of the triangle is (1/2) × 12 × 7 = 42 square units.
When the dimensions of the triangle are increased by a factor of 3, the new base becomes 12 × 3 = 36 units and the new height becomes 7 × 3 = 21 units. Thus, the area of the enlarged triangle is (1/2) × 36 × 21 = 378 square units. Therefore, the area of the triangle increases by a factor of 378/42 = 9.