Deductive Analysis of Area Ratios in Parallel and Similar Configurations
Deductive Analysis of Area Ratios in Parallel and Similar Configurations
Secondary 3
In the diagram below, \(PQRS\) is a trapezium in which \(PQ\) is parallel to \(SR\).
- Prove that \(\Delta PQT\) is similar to \(\Delta RST\).
- Given that \(PQ = 12\text{ cm}\), \(SR = 30\text{ cm}\) and \(QT = 5\text{ cm}\),
- calculate \(ST\) ,
- find the value of \(\frac{\text{Area of}\hspace{0.5em} \Delta PQT}{\text{Area of}\hspace{0.5em} \Delta RST}\) ,
- find the value of \(\frac{\text{Area of}\hspace{0.5em} \Delta PQT}{\text{Area of}\hspace{0.5em} \Delta QTR}\) .
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Answer:\(\text{(i)}\ \triangle PQT\sim\triangle RST\text{ (AA)}\) \(\text{(ii)(a)}\ ST=12.5\text{ cm}\) \(\text{(ii)(b)}\ \dfrac{4}{25}\) \(\text{(ii)(c)}\ \dfrac{2}{5}\)
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