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If the given triangles are similar, calculate the missing length.


*x* = 8.4

*x* = 16.8

*x* = 23.6

*x* = 30.25

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:

\[
\frac{x}{12} = \frac{7}{5} \rightarrow x \cdot Proportion sides

To double check equation alignment before concluding.
Looking at the triangles again:

The given triangles have these corresponding sides:
- Triangle 1: 7, 12, \(x\) (left triangle)
- Triangle 2: 12, 7, 5 (right triangle)

### Correct Approach:

Let's pair corresponding sides correctly:

\[
\frac{x}{12} = \frac{7}{5}
\]

Cross-multiplying:
\[
5x = 12 \times 7
\]

Calculate:
\[
x = \frac{84}{5} = 16.8
\]

### Answer:
- \(x = 16.8\) is correct missing length!

Need more? Explore these:
1. Why triangles similarity applies?
2. Scale used among right ones!
3. If Alt. sides, would change answers?
4. Ratios solved any triangle.
5. Sides if both scalene, equilateral shifts?

**Tip:** Always check units converting equations stay matched ratios match sides!

If the given triangles are similar, calculate the missing length.

Learn how to calculate the missing length in similar triangles using the properties of proportions and the similarity theorem. This detailed step-by-step solution covers the proportionality of corresponding sides, cross-multiplication, and solving equations, making it suitable for students in Grades 8-10.

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