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Fabian used a ratio table to show the original dimensions of a rectangle and the dimensions when the rectangle is changed by a scale factor. He forgot to enter the length of the new rectangle.

\begin{tabular}{|c|c|c|}
\hline
Scale factor & 1 & 2.5 \\
\hline
Width & 6 & 15 \\
\hline
Length & 9 & \\
\hline
\end{tabular}

Which length is missing from Fabian's table?

A. 3.6
B. 11.5
C. 21.6
D. 22.5



Answer :

GinnyAnswer
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].

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