In the triangle $PQR$, $PQ = 9$ cm, $PR = 15$ cm and $K$ is a point on the side $PR$ such

Question

In the triangle $PQR$, $PQ = 9$ cm, $PR = 15$ cm and $K$ is a point on the side $PR$ such that $\angle PQK = \angle PRQ$. Show that $\Delta PQK$ is similar to $\Delta PRQ$. Hence, find the length of $PK$. Given that the area of $\Delta PQK$ is $19.4$ cm$^2$, calculate the area of $\Delta PRQ$, the area of $\Delta KRQ$.

Accepted Answer

$\text{(i)}\ \triangle PQK\sim\triangle PRQ\text{ (AA)}$ $\text{(ii)}\ PK=5.4\text{ cm}$ $\text{(iii)(a)}\ 53.9\text{ cm}^2$ $\text{(iii)(b)}\ 34.5\text{ cm}^2$

IP2U8 Exercise Q5

IP2U8 Exercise Q5

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