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To solve for \( m \) given that the shapes are similar, we need to set up a proportion based on the corresponding sides of the similar shapes.

The given dimensions are:
- Smaller shape: 8 (height), \( x \) (base)
- Larger shape: 10 (height), 15 (base)

Since the shapes are similar, the ratios of their corresponding sides are equal. Thus, we have:
\[
\frac{8}{10} = \frac{x}{15}
\]

We can solve for \( x \):
\[
\frac{8}{10} = \frac{x}{15} \implies 8 \cdot 15 = 10 \cdot x \implies 120 = 10x \implies x = \frac{120}{10} = 12
\]

Now, we know that the base of the smaller shape is 12. The length \( m \) is the difference between the base of the larger shape and the base of the smaller shape:
\[
m = 15 - 12 = 3
\]

Thus, \( m = 3 \).

Would you like any more details or have any questions?

Here are some related questions for further practice:

1. How do you verify that two shapes are similar?
2. What is the importance of proportions in similar shapes?
3. How can you find missing dimensions in similar figures using proportions?
4. What are some real-life applications of similar shapes?
5. Can similar shapes be different sizes? Why or why not?

**Tip:** When dealing with similar shapes, always remember to compare corresponding sides and set up a proportion to solve for missing dimensions.

Find m, given the shapes are similar. The dimensions of the smaller shape are 8 (height) and x (base), and the dimensions of the larger shape are 10 (height) and 15 (base).

Learn how to solve for the missing length m in similar shapes using proportions. Given the dimensions of a smaller and a larger shape, apply the proportion formula to find the unknown value. Suitable for students in Grades 8-10.

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