Question

17. Fie triunghiul echilateral ABC cu aria egală cu 36radical din3 u.a. Să se calculeze:
a) perimetrul triunghiului ABC;
b) raza cercului circumscris triunghiului.​

Answer 1

   

$\displaystyle\\A=\frac{l^2\sqrt{3} }{4}=36\sqrt{3}~cm^2\\\\l^2\sqrt{3} =4\times36\sqrt{3}\\\\l^2\sqrt{3} =144\sqrt{3}~~~\Big|~:\sqrt{3}\\\\l^2=144\\\\l=\sqrt{144}=\boxed{\bf12~cm}\\\\{\bf~a)}\\\\P\Delta ABC=3\times l=3\times 12=\boxed{\bf36~cm}\\\\{\bf~b)}\\\\R=\frac{l}{\sqrt{3}}=\frac{12}{\sqrt{3}}=\frac{12\sqrt{3}}{3}=\boxed{\bf4\sqrt{3}~cm}$