The diagram in the image involves parallel lines and can be solved using the Triangle Proportionality Theorem, also known as the Basic Proportionality Theorem. This theorem states that if a line is parallel to one side of a triangle and intersects the other two sides, it divides those two sides proportionally.

Key Elements:

• $WU$ is the full length (35).
• $VT$ is the length on the parallel lines (24).
• $WS$ is the other part, given as 22.

We want to find $TU$, which is the missing part of line segment $WU$.

Steps:

Using the Triangle Proportionality Theorem:

$\frac{TV}{TU} = \frac{WS}{WU}$

Substitute the values we know:

$\frac{24}{TU} = \frac{22}{35}$

Now solve for $TU$:

$24 \cdot 35 = 22 \cdot TU$

$840 = 22 \cdot TU$

$TU = \frac{840}{22} = 38.18 \, (\text{rounded to two decimal places})$

Final Answer:

$TU \approx 38.18$

Would you like any additional details or explanations?

Here are 5 relative questions:

1. What is the Triangle Proportionality Theorem?
2. How do parallel lines affect proportionality in triangles?
3. Can the Triangle Proportionality Theorem be applied to non-triangular shapes?
4. What are other methods to solve for unknown sides in similar triangles?
5. How does the Pythagorean theorem relate to this type of problem?

Tip: Always check if the given sides or angles are proportional when dealing with parallel lines and triangles!