2003 Fermat Problem 23

Three faces of a rectangular box meet at a corner of the box. The centres of these faces form the vertices of a triangle having side lengths of 4 cm, 5 cm and 6 cm. The volume of the box, in \text{cm}^3, is

\textbf{(A)}\ 45\sqrt{3}\quad \textbf{(B)}\ 45\sqrt{6}\quad \textbf{(C)}\ 90\sqrt{6}\quad \textbf{(D)}\ 125\quad \textbf{(E)}\ 120\sqrt{2}

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