To determine the missing length in Fabian's ratio table, let's follow these steps:
1. Understand the relationship described by the scale factors: The ratio table describes how each dimension changes when multiplied by the given scale factors.
2. Identify the original dimensions and their corresponding scaled dimensions:
- Original width (corresponding to scale factor 1): 6 units
- New width (corresponding to scale factor 2.5): 15 units
- Original length (corresponding to scale factor 1): 9 units
- Missing new length (corresponding to scale factor 2.5): [tex]\(L\)[/tex]
3. Setup proportions for the width to understand the scaling:
- When the width changed from 6 to 15, we can confirm that the width has been scaled by a factor of 2.5 (as expected by the scale factor).
4. Apply the scale factor to the original length:
- The same scale factor is applied to the lengths. Therefore:
[tex]\[
L = \text{Original length} \times \text{Scale factor}
\][/tex]
- Substitute the known values:
[tex]\[
L = 9 \times 2.5
\][/tex]
5. Calculate:
- [tex]\( 9 \times 2.5 = 22.5 \)[/tex]
Thus, the missing length in Fabian's table is [tex]\( \boxed{22.5} \)[/tex].
