a) Bisectoarea unui unghi imparte unghiul in 2 unghiuri congruente.
Deci [tex]m(BCE)= \frac{m(\ \textless \ ACB)}{2}= \frac{60~(grade)}{2}=30~(grade). [/tex]
b) [tex] P_{ABC}=3l\Rightarrow l= \frac{ P_{ABC} }{3}=12(cm). \\ A_{ABC}= \frac{ l^{2} \sqrt{3} }{4} = \frac{144 \sqrt{3} }{4}=36 \sqrt{3}(cm^{2}). \\ \\ (l~este~lungimea~laturii~triunghiului) [/tex]
c) Fie D∈(BC) astfel incat ED _|_ BC (perpendicular). Distanta de la E la BC este DE. (d(E,BC)=DE)
[tex] A_{ABC}= \frac{CE*AB}{2}\Rightarrow CE= \frac{2* A_{ABC} }{AB}= \frac{2* 36\sqrt{2} }{12} = 6\sqrt{2}~(cm). [/tex]
In triunghiul CED, dreptunghic in D, cateta [DE] se opune unghiului de 30* => [tex]DE= \frac{CE}{2} = \frac{ 6\sqrt{2} }{2}=3 \sqrt{2}~(cm). [/tex]
[tex]Deci~\boxed{d(E,BC)=3 \sqrt{2}~cm}. [/tex]
