Question

urgent ex 6 tot dau inima si coroana ​

Answer 1

Răspuns:

Explicație pas cu pas:

$A_{VAC}=\frac{VO\cdot AC}{2} =A_{ABDC}$

AC=12√2

$A_{ABCD}=12^{2} =144$

$A_{VAC}=\frac{VO\cdot AC}{2} =144\\\frac{VO\cdot 12\sqrt{2} }{2} =144$

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

$\frac{VP}{VO} =\frac{VT}{VA}= \frac{PT}{OA}\\\\ \frac{2}{3} =\frac{VT}{6\sqrt{10} } =\frac{PT}{6\sqrt{2} }$

VT=4√10

PT=4√2

InΔVPT dr

$PS=\frac{VP\cdot PT}{VT} =\frac{8\sqrt{2}\cdot 4\sqrt{2} }{4\sqrt{10} } =\frac{8\sqrt{10} }{5}$