Question

Rog seriozitate! Urgent!​

Answer 1

Răspuns:

Explicație pas cu pas:

a. $A_{AMNC}=A_{ABCD}-A_{ABM}-A_{ADN}$

$A_{ABCD}=l^2$

DC=l

$DN=DC-NC=DC-\frac{DC}{3} =\frac{2l}{3} =BM$

$A_{ADN}=A_{ABM}=\frac{l\cdot \frac{2l}{3} }{2} =\frac{l^2}{3}$

$A_{AMNC}=l^2-\frac{l^2}{3} -\frac{l^2}{3} =\frac{l^2}{3}$

b. Fie MP⊥AN

Facem prin aria in 2 moduri in ΔAMN

$A_{MNC}=\frac{MC\cdot CN}{2} =\frac{l^2}{18}$

$A_{AMN}=A_{AMNC}-A_{MNC}=\frac{l^2}{3} -\frac{l^2}{18} =\frac{5l^2}{18} =\frac{MP\cdot AN}{2}$

Aflam AN inΔAND aplicand Pitagora

AN²=AD²+DN²

$AN^2=l^2+\frac{4l^2}{9} =\frac{13l^2}{9} \\\\AN=\frac{l\sqrt{13} }{3}$

$A_{AMN}=\frac{5l^2}{18} =\frac{MP\cdot AN}{2}\\\\\frac{5l^2}{18} =\frac{MP\cdot l\sqrt{13} }{6} \\\\MP=\frac{5l}{3\sqrt{13} } =\frac{5l\sqrt{13} }{39}$

Sa mai verifici odata tu calculele