Question

find tu. tu = submit

Explanation:

Step1: Use the mid - segment theorem

The mid - segment theorem states that a mid - segment of a triangle (a segment connecting the midpoints of two sides of a triangle) is parallel to the third side and half its length. Here, \(QT\) is a mid - segment of \(\triangle RUS\).

Step2: Find the length of \(UR\)

We know that \(UR = 21\) (given) and \(QR=7\). But since \(QT\) is a mid - segment, we can also use the proportion. Let's use the property of similar triangles (by the basic proportionality theorem or mid - segment concept).
The ratio of the sides of \(\triangle TQS\) and \(\triangle RUS\) (since \(QT\parallel UR\)) gives us the relationship.
We know that \(\frac{TU}{24}=\frac{UR - QR}{UR}\). Wait, another approach: Since \(QT\) is a mid - segment (because of the arrow marks indicating parallelism and mid - point like ratios, assume \(Q\) is the mid - point of \(UR\) and \(T\) is the mid - point of \(US\)).
By the mid - segment theorem, if we consider the line parallel to a side of a triangle cutting the other two sides proportionally.
Let's use the formula for the length of a line segment in a triangle with a parallel line.
We know that \(\frac{TU}{24}=\frac{21}{21 + 7}\) (using the basic proportionality theorem, if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally).

$$
LATEXBLOCK0
$$

Answer:

\(18\)