The image shows a math problem involving similar figures, specifically comparing two triangles to find a missing side length. Here's a detailed solution for the problem:

Problem Analysis:

1. The problem involves two similar triangles:
   • Triangle 1: Sides are given as 18 (height) and 24 (base).
   • Triangle 2: One side length is missing (denoted as "x"), and the other given side is 40.

Solution:

Since the triangles are similar, their corresponding sides are proportional. This means the ratio of the sides of the first triangle will be the same as the ratio of the sides of the second triangle.

Set up the proportion using the sides: $\frac{18}{x} = \frac{24}{40}$

Cross-multiply to solve for $x$: $18 \times 40 = 24 \times x$

$720 = 24x$

Now, solve for $x$: $x = \frac{720}{24}$

$x = 30$

Answer:

The missing side length $x$ is 30 units.

Would you like further details or have any questions about this solution?

Related Questions:

1. What are similar triangles, and how do their properties help in solving problems like this?
2. How do you determine if two triangles are similar based on side lengths and angles?
3. Can the method of setting proportions be used for figures other than triangles?
4. How do scaling factors affect the dimensions of similar geometric figures?
5. What are other real-world applications of similar triangles in measurements?

Tip: Always check if the triangles are similar by comparing their corresponding angles or side ratios before setting up proportions.