In the diagram, $PQ$ is parallel to $ST$ and $XY$ is parallel to $RT$. Given that \(PRT

Question

In the diagram, $PQ$ is parallel to $ST$ and $XY$ is parallel to $RT$. Given that $PRT$, $QRXS$ and $SYT$ are straight lines. Prove that $\Delta PQR$ and $\Delta YSX$ are similar. Given that $QR = 4$ cm, $RX = 2$ cm, $XS = 8$ cm and $XY = 16$ cm. Find the numerical value of $\frac{QR}{SR}$, $\frac{\text{Area of}\hspace{0.5em} \Delta SXY}{\text{Area of}\hspace{0.5em} \Delta SXT}$, $\frac{\text{Area of}\hspace{0.5em} \Delta PQR}{\text{Area of}\hspace{0.5em} \Delta TSR}$. Hence, calculate the area of $\Delta TSR$, given that the area of $\Delta PQR$ is $25$ cm$^2$.

Accepted Answer

$\text{(i)}\ \triangle PQR\sim\triangle YSX\text{ (AA)}$ $\text{(ii)(a)}\ \dfrac{2}{5}$ $\text{(ii)(b)}\ \dfrac{4}{5}$ $\text{(ii)(c)}\ \dfrac{4}{25}$ $\text{(iii)}\ 156.25\text{ cm}^2$

IP2U8 Exercise Q6

IP2U8 Exercise Q6

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