To find the third proportional to two given numbers \(a\) and \(b\), we need to find a number \(c\) such that the ratio \( \frac{a}{b} \) is equal to the ratio \( \frac{b}{c} \).

Given:
- \( a = 7 \)
- \( b = 13 \)

We need to find \( c \) such that:

\[
\frac{7}{13} = \frac{13}{c}
\]

Cross-multiplying gives:

\[
7c = 13 \times 13
\]

\[
7c = 169
\]

Solving for \( c \):

\[
c = \frac{169}{7} = 24.14 \, \text{(approximately)}
\]

Therefore, the third proportional to 7 and 13 is approximately **24.14**.

Would you like more details or have any questions?

Here are five related questions:
1. What is the third proportional to 5 and 10?
2. How is the mean proportional between two numbers calculated?
3. What is the geometric mean of 7 and 13?
4. Can the third proportional be a fraction?
5. How is the concept of proportionality used in geometry?

**Tip:** Always cross-multiply to solve proportions involving unknowns effectively.

Learn how to find the third proportional to 7 and 13 with a step-by-step solution. This problem covers key concepts of proportionality and cross-multiplication. Suitable for students in Grades 7-9.

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