Question

8 △stu-△vsu

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle STU\sim\triangle VSU\), we have the proportion \(\frac{SU}{TU}=\frac{VU}{SU}\).

Step2: Substitute the given values

Given \(TU = 2\) and \(VU=18\), substituting into the proportion \(\frac{SU}{2}=\frac{18}{SU}\).
Cross - multiply to get \(SU^{2}=2\times18 = 36\).

Step3: Solve for \(SU\)

Take the square root of both sides. Since \(SU>0\) (length), \(SU=\sqrt{36}=6\).

Answer:

\(6\)