To solve this problem, we need to use the property of similar triangles, which states that the corresponding sides of similar triangles are in proportion.

Given the triangles in the image:

• The left triangle has sides $7$, $12$, and $x$.
• The right triangle has sides $7$, $12$, and $5$.

Since these triangles are similar, we can set up a proportion using the corresponding sides.

Step-by-step Solution:

1. Set up the proportion:
   $\frac{7}{12} = \frac{x}{5}$

2. Cross multiply to solve for $x$:
   $7 \times 5 = 12 \times x$ $35 = 12x$

3. Solve for $x$:
   $x = \frac{35}{12}$ $x \approx 2.92$

It seems that the missing side calculation needs another approach. Let’s try setting up the correct proportion again:

For a correct approach, the sides should be related as follows: