Explicație pas cu pas:
a) ME ⊥ AB, MF ⊥ AC
[tex]A_{(ABC)} = A_{(AMB)} + A_{(AMC)} \\ = \frac{ME\cdot AB}{2} + \frac{MF\cdot AC}{2} \\ = \frac{ME\cdot AB + MF\cdot AC}{2} [/tex]
→
[tex]ME\cdot AB + MF\cdot AC = 2\cdot A_{(ABC)} \\ [/tex]
b) AB ≡ AC = a
[tex]A_{(ABC)} = \frac{{a}^{2} \sqrt{3} }{4} \\ [/tex]
[tex]ME\cdot AB + MF\cdot AC = (ME + MF)\cdot a \\ = 2\cdot \frac{ {a}^{2} \sqrt{3} }{4} \\ = > ME + MF = \frac{a \sqrt{3} }{2} [/tex]
