[tex]A=L*l \\ A=BC*AB \\ \\ BC^2 = AC^2 - AB^2 \\ \\ BC^2 = (\dfrac{5}{4}BC)^2 - 36 \\ \\ BC^2 = \dfrac{25}{16}BC^2 - 36 \ \ | *16 \\ 16BC^2=25BC^2-576 \\ \\ -9BC^2 = -576 \ | *(-1) \\ 9BC^2=576 \\ BC^2=576:9 \\ BC^2=64 \\ BC= \sqrt{64} \\ BC=8 \ cm \\ \\ A=BC*AB \\ A = 8 * 6 \\ \boxed{A = 48\ cm^2}[/tex]
