Questions: Find TU.

Find TU.
Transcript text: Find $T U$. \[ T U= \] $\square$
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Solution

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Find \(TU\). Calculate the ratio between the sides of the two similar triangles. The two triangles \( \triangle SQR \) and \( \triangle STU \) are similar. The ratio of corresponding sides is \( \frac{SR}{SU} = \frac{QR}{TU} = \frac{SQ}{ST}\). \(SU = SR + RU = 30 + 45 = 75 \). \(QR = 7 \). \(SR = 30\). Use the ratio of corresponding sides to find TU. \( \frac{SR}{SU} = \frac{QR}{TU}\) \( \frac{30}{75} = \frac{7}{TU}\) \(TU = \frac{75 \times 7}{30}\) \(TU = \frac{525}{30}\) \(TU = \frac{52.5}{3}\) \(TU = 17.5 \)

\( \boxed{TU=17.5} \)

\(TU=17.5\)

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