Answer:
The area increased by a factor of 25, from 6 in^2 to 150 in^2, when the scale factor for the sides was 5.
Explanation:
The area increased from 6 in^2 to 150 in^2 when the Original triangle was scaled by a factor of 5 (in inches):
Original Scaled Factor
3 15 5
5 25 5
4 20 5
Area (in^2)
6 150 25
The larger increase in the sale factor for area is due to the area equation for a triangle: Area = (1/2)b*h. Since both the base and height both increase by a factor of 5, the are increses by a factor of 25:
Original: A = (1/2)b*h
Scaled by 5: A = (1/2)((5b)*(5h)) or (1/2)(25)(b*h) [(1/2)b*h is the original area)
Area(scaled) = 25*A(original)