Question

find the length of the indicated line segment.
su = \square

Explanation:

Step1: Use the property of similar triangles or proportional segments

Since the lines are parallel, we can set up a proportion. Let's assume the segments are divided proportionally. We have \(\frac{8}{12}=\frac{10}{SU}\) (by the basic proportionality theorem for parallel - cut transversals).

Step2: Solve the proportion for \(SU\)

Cross - multiply the proportion \(\frac{8}{12}=\frac{10}{SU}\). We get \(8\times SU = 12\times10\). Then \(8SU=120\). Divide both sides by 8: \(SU=\frac{120}{8}\).

Answer:

\(15\)