Răspuns:
Explicație pas cu pas:
in ΔABC dreptunghic:
[tex]AB^{2} =BC^{2} -AC^{2} =100-64=36= > AB=6cm\\AM=AB-MB=6-2=4cm[/tex]
in ΔAMC dreptunghic:
[tex]MC^{2}=AM^{2} +AC^{2} =16+64=80= > MC=4\sqrt{5}cm[/tex]
[tex]Aria_{ABC}=\frac{AB*AC}{2}=\frac{6*8}{2}=24cm^{2}\\Aria_{AMC}=\frac{AM*AC}{2}=\frac{4*8}{2}=16cm^{2}\\Aria_{BMC}=Aria_{ABC}-Aria_{AMC} =24-16=8cm^{2}[/tex]
[tex]Aria_{AMC}=\frac{h_{1}*MC}{2}\\= > h_{1}=\frac{2*16}{4\sqrt{5} }=\frac{8}{\sqrt{5} }cm\\Aria_{BMC}=\frac{h_{2}*MC}{2}\\= > h_{2}=\frac{2*8}{4\sqrt{5} }=\frac{4}{\sqrt{5} }cm[/tex]
[tex]h_{1}+h_{2}=\frac{8}{\sqrt{5} }+\frac{4}{\sqrt{5} }=\frac{12}{\sqrt{5} }\\\frac{12}{\sqrt{5} }*\frac{3}{16} *\frac{16}{3}=\frac{16}{3}*\frac{9}{4\sqrt{5} }=\frac{16}{3}*\sqrt{\frac{81}{80} } > \frac{16}{3}\\= > h_{1}+h_{2} > \frac{16}{3}[/tex]
