Răspuns:
Explicație pas cu pas:
[tex]A_{VAC}=\frac{VO\cdot AC}{2} =A_{ABDC}[/tex]
AC=12√2
[tex]A_{ABCD}=12^{2} =144[/tex]
[tex]A_{VAC}=\frac{VO\cdot AC}{2} =144\\\frac{VO\cdot 12\sqrt{2} }{2} =144\\[/tex]
VO=12√2
VP+PO=12√2
3PO=12√2
PO=4√2
VP=8√2
d(P,VA)=PS
VA²=VO²+OA²
VA²=288+72=360
VA=6√10
Fie PT║OA
[tex]\frac{VP}{VO} =\frac{VT}{VA}= \frac{PT}{OA}\\\\ \frac{2}{3} =\frac{VT}{6\sqrt{10} } =\frac{PT}{6\sqrt{2} }[/tex]
VT=4√10
PT=4√2
InΔVPT dr
[tex]PS=\frac{VP\cdot PT}{VT} =\frac{8\sqrt{2}\cdot 4\sqrt{2} }{4\sqrt{10} } =\frac{8\sqrt{10} }{5}[/tex]
