$
\eqalign{
& O_{\Delta AQC} = \frac{1}
{2} \cdot 7 \cdot 4 \cdot \sin \left( \alpha \right) \cr
& O_{\Delta CPB} = \frac{1}
{2} \cdot 3 \cdot \left( {4 + BQ} \right) \cdot \sin \left( \alpha \right) \cr
& \frac{1}
{2} \cdot 3 \cdot \left( {4 + BQ} \right) \cdot \sin \left( \alpha \right) = \frac{1}
{2} \cdot 7 \cdot 4 \cdot \sin \left( \alpha \right) \cr
& 3 \cdot \left( {4 + BQ} \right) = 7 \cdot 4 \cr
& 3 \cdot \left( {4 + BQ} \right) = 28 \cr
& 4 + BQ = 9\frac{1}
{3} \cr
& BQ = 5\frac{1}
{3} \cr}
$
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