4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bb1becd5-96c1-426d-9b85-4bbc4a61af27-08_287_689_255_625}
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\caption{Figure 1}
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Figure 1 shows a sketch of a triangle \(A B C\) with \(A B = 3 x \mathrm {~cm} , A C = x \mathrm {~cm}\) and angle \(C A B = 60 ^ { \circ }\)
Given that the area of triangle \(A B C = 24 \sqrt { 3 }\)
- show that \(x = 4 \sqrt { 2 }\)
- Hence find the exact length of \(B C\), giving your answer as a simplified surd.