Question

find tv.
tv =
submit
work it out
not feeling ready yet? these can help
side lengths and angle measures in similar figures

Explanation:

Step1: Use the mid - segment theorem

Since \(US\parallel VR\) and \(US\) is a mid - segment (marked by the same tick marks), we can use the proportion \(\frac{VU}{UT}=\frac{RS}{ST}\). Given \(VU = 8\), \(ST=34\), \(RS = 17\). Let \(UT=x\). Then \(\frac{8}{x}=\frac{17}{34}\).

Step2: Solve the proportion

Cross - multiply: \(17x=8\times34\). So \(x=\frac{8\times34}{17}\). Since \(\frac{34}{17} = 2\), then \(x = 16\).

Step3: Calculate \(TV\)

\(TV=VU + UT\). Substitute \(VU = 8\) and \(UT = 16\). So \(TV=8 + 16\).

Answer:

\(24\)