2026 MSHS P2 Q1

Do not use a calculator in this question.

In triangle \(ABC\), \(AB=(6+\sqrt5)\) cm and \(\angle ABC=30^\circ\). Given that the triangle has an area of \(\dfrac14(32-5\sqrt5)\) cm², find the exact length of \(BC\). Give your answer in the form \((a+b\sqrt5)\), where \(a\) and \(b\) are integers.[4]