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In the diagram below, SR = PQ = 20 and RT:TS = 2:5. Find UV.

 

 Feb 24, 2024
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\(\overline{TR}=20*\frac{2}{5+2}=\frac{40}{7}\).

Set the value of \(\overline{UV}=x\).

 \(\because UVQP\sim TRVU\).

\(\therefore \frac{TR}{UV}=\frac{UV}{PQ}\)

\(\therefore \frac{\frac{40}{7}}{x}=\frac{x}{20}\)

\({x}^{2}=\frac{800}{7}\)

\(x=\frac{\sqrt{800}}{\sqrt{7}}=\frac{20\sqrt{14}}{7}\)

 Feb 24, 2024

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