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In the diagram, R\(\hat{P}\)Q = Q\(\hat{R}\)Y, P\(\hat{Q}\)R = R\(\hat{Y}\)Q, |QP| = 8 cm, |QY| =...

Mathematics
WAEC 2004

In the diagram, R\(\hat{P}\)Q = Q\(\hat{R}\)Y, P\(\hat{Q}\)R = R\(\hat{Y}\)Q, |QP| = 8 cm, |QY| = 4 cm, and |RY| = 5 cm. Find |QR|.

  • A. 2.0cm
  • B. 2.5cm
  • C. 6.4cm
  • D. 10.0cm
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Correct Answer: Option C
Explanation

\(\frac{PR}{QR} = \frac{QR}{QY} = \frac{QP}{YR}\) (SSS Congruence)

\(\frac{QR}{4} = \frac{8}{5}\)

\(QR = \frac{4 \times 8}{5}\)

= 6.4 cm

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