3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{52966963-2e62-4361-bcd5-a76322f8621e-08_1141_810_287_148}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{52966963-2e62-4361-bcd5-a76322f8621e-08_752_803_484_1114}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
The uniform triangular lamina \(A B C\), shown in Figure 1, has height \(9 y\), base \(B C = 6 x\), and \(A B = A C\)
The points \(P\) and \(Q\) are such that \(A P : P C = A Q : Q B = 2 : 1\)
The lamina is folded along \(P Q\) to form the folded lamina \(F\)
The distance of the centre of mass of \(F\) from \(P Q\) is \(d\)
- Show that \(d = \frac { 16 } { 9 } y\)
The folded lamina is suspended from \(P\) and hangs freely in equilibrium with \(P Q\) at an angle \(\alpha\) to the downward vertical.
Given that \(\tan \alpha = \frac { 64 } { 81 }\) - find \(x\) in terms of \(y\)