Respuesta :

We know from Euclidean Geometry and the properties of a centroid that GC=2GM. Now GM=sin60*GA=[tex] \sqrt{3} [/tex]. Hence CM=GC+GM=3*[tex] \sqrt{3} / [/tex]. Now, since GM is normal to AB, we have by the pythagoeran theorem that:
[tex]AC^2=AM^2+GM^2=BM^2+GM^2=BC^2[/tex]
Hence, we calculate from this that AC^2= 28, hence AC=2*[tex] \sqrt{7} [/tex]=BC. Thus, the perimeter of the triangle is 2+4*[tex] \sqrt{7} [/tex].
Ver imagen TheSandman1337