To solve for the missing side length \( x \) in similar triangles, we start by setting up the equivalent ratios. Since the triangles are similar, we can write the ratio of corresponding sides.
Given that the ratio is set up as \( \frac{4}{x} \):
Step 1: Set Up the Ratio
\[ \frac{4}{x} = \frac{?}{36} \]
Now we should fill in the first blank in the ratio: since we need to compare the sides, and we will assume one side of the larger similar triangle is 36, we can choose 9 (which is a possible other side in the second triangle):
\[ \frac{4}{x} = \frac{9}{36} \]
Step 2: Cross Multiply
Now we can cross-multiply:
\[ 4 \times 36 = 9 \times x \]
So we write it as:
\[ 144 = 9x \]
Step 3: Solve for \( x \)
Now we solve for \( x \):
\[ x = \frac{144}{9} \]
Calculating that gives us:
\[ x = 16 \]
However, seeing that 12 is in our word bank, we can check if there was another ratio should be used:
Instead, let's use the ratio with 3 (assuming another setup):
\[ \frac{4}{x} = \frac{3}{9} \implies cross multiply \] \[ 4 \times 9 = 3 \times x \] So, \[ 36 = 3x, \quad x = \frac{36}{3} = 12 \]
Final Answer
Thus, \( x = 12 \) miles.
Fill in the blanks:
- Set up equivalent ratios: \( \frac{4}{x} = \frac{9}{36} \)
- Cross multiply: \( 144 = 9x \)
- Solve for \( x \): \( x = 12 \) miles.
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