Final answer:
To find the corresponding side of a similar polygon with sides 3ft and 9ft, we must apply the scale factor of 3. Multiplying each option by 3, we find that 6ft is the correct answer when the smaller side is 2ft.
Step-by-step explanation:
The question asks to find the side corresponding to sides of 3ft and 9ft in similar polygons. When two polygons are similar, the lengths of their corresponding sides are proportional. So, if one side of the smaller polygon is 1ft, 2ft, 4ft, or 6ft, we have to determine which of these when multiplied by the same factor (scale factor) used to enlarge 3ft to 9ft, will produce the correct corresponding length.
Here, the scale factor is 3 (since 9ft / 3ft = 3). We can calculate the corresponding side by multiplying each of the given options by 3:
- 1ft × 3 = 3ft
- 2ft × 3 = 6ft
- 4ft × 3 = 12ft
- 6ft × 3 = 18ft
The correct answer is (d) 6ft, as when 2ft is multiplied by the scale factor of 3, it gives us 6ft.