The problem involves two similar triangles, and you're asked to find the value of $z$.

Given dataThe problem involves two similar triangles, and you're asked to find the value of $z$.

Given

• The sides of the larger triangle are $16$ cm (the longer base) and $z$ cm (the unknown side corresponding to the longer leg of the smaller triangle).
• The sides of the smaller triangle are $10$ cm (the shorter base) and $3.6$ cm (the shorter leg).

Since the triangles are similar, the ratio of corresponding sides will be equal. Therefore, we can set up the following proportion:

$\frac{z}{3.6} = \frac{16}{10}$

Now, let's solve for $z$.

First, simplify the ratio on the right-hand side:

$\frac{16}{10} = 1.6$

So, we have:

$\frac{z}{3.6} = 1.6$

To find $z$, multiply both sides by 3.6:

$z = 1.6 \times 3.6 = 5.76 \text{ cm}$

So, the value of $z$ is $5.76$ cm.

Would you like more details on this calculation or have any questions?

Here are five related questions to expand your understanding:

1. How do you determine if two triangles are similar?
2. What other methods can be used to solve problems involving similar triangles?
3. What is the relationship between the angles in similar triangles?
4. How does changing one side of a similar triangle affect the corresponding side in the other triangle?
5. How would the solution change if the triangles were congruent instead of similar?

Tip: Always double-check the similarity ratio you use, ensuring that corresponding sides are correctly matched before solving.