Question

fie triunghiul echilateral abc cu latura de lungime a.daca d∈bc astfel incat db=bc si e∈ac astfel incat ce=ac,calculati perimetrul triunghiului ade

Answer 1

$AE=EC= \frac{AC}{2} = \frac{a}{2} \\ BD=DC$
⇒ AD inaltime ⇒ 
$AD= \frac{a \sqrt{3} }{2}$
AE=EC ; BD=DC ⇒ DE linie mijlocie ⇒ $DE= \frac{AB}{2} = \frac{a}{2}$
$P _{ADE} =AD+DE+AE= \frac{a \sqrt{3} }{2} +\frac{a}{2}+\frac{a}{2} = \frac{2a+a \sqrt{3} }{2} = \\ = \frac{a(2+ \sqrt{3}) }{2}$