To find the length of the side \( x \) in Triangle 1, we start by using the fact that Triangle 1 is a scale drawing of Triangle 2. This means that the sides of Triangle 1 are proportional to the sides of Triangle 2.
Given:
- Triangle 1 sides: \( 4 \), \( x \), \( 6 \)
- Triangle 2 sides: \( 6 \), \( 10.5 \), \( 9 \)
We can set up ratios based on the corresponding sides. Let's take the ratio of the smallest side from Triangle 1 (4) to the smallest side from Triangle 2 (6):
\[ \frac{4}{6} = \frac{2}{3} \]
Now, we can use this ratio to express side \( x \) in terms of the corresponding side from Triangle 2, which is the second smallest side \( 10.5 \).
Setting up the proportion:
\[ \frac{x}{10.5} = \frac{2}{3} \]
To find \( x \), we'll cross multiply:
\[ 3x = 2 \times 10.5 \] \[ 3x = 21 \]
Now, divide both sides by 3:
\[ x = \frac{21}{3} = 7 \]
Thus, the length of side \( x \) is
\[ \boxed{7} \]
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