iran-konkur 2023 Q28

iran-konkur · Other · konkur-riazi_1402_general Sine and Cosine Rules Multi-step composite figure problem
28. In triangle $ABC$, the medians drawn from vertices $B$ and $C$ are perpendicular to each other. If the length of the median drawn from vertex $C$ is $4.5$ and the area of this triangle is $18$, what is the ratio of the lengths of the medians drawn from vertices $B$ and $C$?
(1) $\dfrac{17}{9}$ (2) $\dfrac{19}{9}$ (3) $\dfrac{5}{3}$ (4) $\dfrac{4}{3}$ 
\textbf{28.} In triangle $ABC$, the medians drawn from vertices $B$ and $C$ are perpendicular to each other. If the length of the median drawn from vertex $C$ is $4.5$ and the area of this triangle is $18$, what is the ratio of the lengths of the medians drawn from vertices $B$ and $C$?

(1) $\dfrac{17}{9}$ \hspace{2cm} (2) $\dfrac{19}{9}$ \hspace{2cm} (3) $\dfrac{5}{3}$ \hspace{2cm} (4) $\dfrac{4}{3}$
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