Question

Perimetrul unui triunghi echilateral care are raza cercului inscris in trunghi egala cu 6√6 cm este de ...cm

Answer 1

$\displaystyle r=\frac{A}{p}=\frac{A}{\frac{P}{2}}=\frac{2A}{P}=\frac{2\cdot\frac{\sqrt3}{4}l^2}{3l}}=\frac{\sqrt3l^2}{6l}=\frac{\sqrt3l}{6} \\ \\ l=\frac{6r}{\sqrt3}=\frac{6\cdot 6\sqrt3\sqrt2}{\sqrt3}=36\sqrt2 \\ \\ P=3\cdot36\sqrt2=108\sqrt2$