Question

inaltimea unui triunghi echilateral este radical din 6 aflati perimetrul si aria

Answer 1

[tex]h=\underbrace{\frac{l_{\Delta}\cdot\sqrt3}{2}\;=\;\sqrt6}_{\Rightarrow\;\;l_{\Delta}}=\frac{2\sqrt6}{\sqrt3}=2\sqrt2}\\ \\ P_{\Dellta}=3\cdot2\sqrt2=6\sqrt2(cm)\;\;\;\;\;si\;\;\;\;A_{\Delta}=\frac{(2\sqrt2)^2\sqrt3}{4}=\frac{8\sqrt3}{4}=2\sqrt3(cm^2)[/tex]

Answer 2

h = (a√3)/2⇒ √6=(a√3)/2⇒a=(2√6)/√3

⇒a=(2√6×√3)/3=2√18/3=2√2

Aria= (a×h)/2=(√6×2√2)/2=√12 = 2√3

Perimetrul =3×a=3×2√2=6√2