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This problem involves similar triangles, and the property of similar triangles is that corresponding sides are proportional. Let's label the sides based on the image you provided.

### The given dimensions:
- The base of the larger triangle is \( x \) inches.
- The base of the smaller triangle is 24 inches.
- The base of the smallest triangle is 18 inches.
- The height of the triangle corresponding to the base of 30 inches.

### Using proportionality:

The triangles with bases \( x \) inches, 30 inches, and 24 inches are similar. Therefore, the corresponding sides of these triangles are proportional. We can write the proportion:

\[
\frac{x}{30} = \frac{30}{24}
\]

Now let's solve for \( x \).

\[
x = \frac{30 \times 30}{24}
\]

Let me calculate this.The value of \( x \) is 37.5 inches.

Would you like any further details or clarifications? Here are some related questions to explore this topic further:

1. What are the properties of similar triangles?
2. How do you calculate the ratio between corresponding sides of similar triangles?
3. What are some common applications of similar triangles in real-life situations?
4. How would the calculation change if a different side ratio were given?
5. What are the key differences between similar and congruent triangles?

**Tip:** Always remember to reduce fractions when working with proportions to simplify your calculations.

Find the value of x. Given similar triangles, the base lengths are proportional with values: 30 inches, 24 inches, and 18 inches.

Learn how to find the value of x by solving a proportion involving similar triangles with given base lengths of 30 inches, 24 inches, and 18 inches. This problem involves the use of proportionality in geometry and is suitable for students in Grades 7-10.

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