Explicație pas cu pas:
ΔABC echilateral
M ∈ BC, ME ⊥ AB, MF ⊥ AC
a)
[tex]Aria_{(ABC)} = Aria_{(ABM)} + Aria_{(ACM)} \\ = \frac{ME \times AB}{2} + \frac{MF \times AC}{2} \\ = \frac{ME \times AB + MF \times AC}{2} \\ = > ME \times AB + MF \times AC = 2 \times Aria_{(ABC)}[/tex]
b) AB = AC = l
[tex]ME \times l + MF \times l = 2 \times Aria_{(ABC)} \\ l \times (ME + MF) = 2 \times \frac{{l}^{2} \sqrt{3} }{4} \\ = > ME + MF = \frac{l \sqrt{3} }{2}[/tex]
