Squares in Triangles

Geometry Level 4

Let a triangle \(ABC\) with \(BC = 6 \text{ cm}\), and the area of \(30\text{ cm}^2\). A square \(PQRS \) is inscribed so that points \(S\) and \(R \) is on \(BC\), \(Q\) on \(AC\), and \(P\) on \(AB\) respectively. Find the side length of the square \(PQRS\).

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