To set up the proportion for the reduction of the rectangle, we can compare the corresponding dimensions of the larger and smaller rectangles.
The larger rectangle has dimensions:
- Length = 18 inches
- Width = 8 inches
The smaller rectangle has dimensions:
- Length = x inches
- Width = 3 inches
The two ratios that can be used in the proportion can be written as:
\[ \frac{\text{Length of larger rectangle}}{\text{Length of smaller rectangle}} = \frac{\text{Width of larger rectangle}}{\text{Width of smaller rectangle}} \]
This gives us the proportion:
\[ \frac{18}{x} = \frac{8}{3} \]
Next, we can solve for \(x\) by cross-multiplying:
\[ 18 \cdot 3 = 8 \cdot x \]
Calculating \(18 \cdot 3\):
\[ 54 = 8x \]
Now, divide both sides by 8 to isolate \(x\):
\[ x = \frac{54}{8} = 6.75 \]
Therefore, the value of the missing measure (length of the smaller rectangle) is \(\boxed{6.75}\) inches.
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