6.
Figure 1
Figure 1 shows a sketch of a triangle \(A B C\) with \(A B = 3 x \mathrm {~cm} , A C = 2 x \mathrm {~cm}\) and angle \(C A B = 60 ^ { \circ }\)
Given that the area of triangle \(A B C\) is \(18 \sqrt { 3 } \mathrm {~cm} ^ { 2 }\)
- show that \(x = 2 \sqrt { 3 }\)
- Hence find the exact length of BC, giving your answer as a simplified surd.