Răspuns:
c) 24 m²
d) [tex]2\sqrt{182}[/tex] m²
Explicație pas cu pas:
c) In Δ ABC m(∡C) = 90° AC = BC
⇒ Δ ABC → dreptunghic isoscel
Daca AC = BC, notam laturile AC si BC cu ,,l''
⇒ (T.P.) AB² = AC² + BC²
[tex](4\sqrt{6})^{2}=l^{2}+l^{2}[/tex]
[tex]96=2l^{2}[/tex] ║ ÷ 2
[tex]48=l^{2}[/tex]
[tex]l=\sqrt{48}[/tex]
[tex]l=4\sqrt{3}[/tex]
[tex]A_{ABC}=\frac{4\sqrt{3}*4\sqrt{3}}{2}[/tex]
[tex]A_{ABC}=\frac{48}{2}[/tex]
[tex]A_{ABC}=24[/tex] m²
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d) [tex]A_{ABC}[/tex] = Formula lui Heron
Formula lui Heron = [tex]\sqrt{p(p-a)(p-b)(p-c)}[/tex]
p = semiperimetrul
a, b, c = laturile triunghiului
[tex]p_{ABC}[/tex] = [tex]\frac{6+9+11}{2}[/tex]
[tex]p_{ABC}=\frac{26}{2}[/tex]
[tex]p_{ABC}=13[/tex] m
[tex]A_{ABC}=\sqrt{13(13-11)(13-6)(13-9)}[/tex]
[tex]A_{ABC}=\sqrt{13*2*7*4}[/tex]
[tex]A_{ABC}=\sqrt{728}[/tex]
[tex]A_{ABC}=2\sqrt{182}[/tex] m²
