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We are given the problem where:

\[
\frac{x}{45} = \frac{20}{x}
\]

To solve for \( x \), let's follow these steps:

### Step 1: Cross-multiply
\[
x \cdot x = 45 \cdot 20
\]
\[
x^2 = 900
\]

### Step 2: Solve for \( x \)
Take the square root of both sides:
\[
x = \sqrt{900}
\]
\[
x = 30
\]

So, the positive value of \( x \) is **30**.

Would you like any further details or have any questions?

Here are 5 related questions to expand on this topic:
1. What is the general method for solving proportions?
2. How do you solve for \( x \) when dealing with more complex ratios?
3. Can a ratio ever have a negative value for \( x \)?
4. How can cross-multiplication be applied in real-world problems?
5. What are some different ways to verify the solution to a proportion?

**Tip:** Always remember to check the final solution by substituting it back into the original equation to ensure accuracy!

Work out the positive value of x that means that x : 45 is equivalent to 20 : x.

Learn how to solve the proportion problem where x : 45 is equivalent to 20 : x. This problem involves key mathematical concepts like cross-multiplication and square roots, making it ideal for students in Grades 8-10.

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