Question

Triunghius Echilateral
Aria=36 radical din 3
aflati:
Latura , perimetrul , inaltimea , r , R

Answer 1

A=l²√3/4 36√3=l²√3/4 36√3 *4=l²√3 l²=36*4 l=6*2=12 P=3*l=3*12=36 H=l√3/2=6√3 R=l/√3=6/√3 r=l√3/6=√3

Answer 2

Fie A, B si C laturile triunghiului echilateral
Fie AM inaltime si med in ΔABC
Arie=36√3
$\frac{l ^{2} \sqrt{3} }{4}$=36
$l^{2} \sqrt{3} =144 \sqrt{3}$
$l^{2} =144$ ⇒ l=12
P=l·3=12·3=36
TP: ⇒[tex] AB^{2} = BM^{2} + AM^{2} 144=36+AM^{2} AM^{2}=108[/tex] ⇒ AM=$6 \sqrt{3}$
r=$\frac{AM}{3}= \frac{6 \sqrt{3} }{3} =2 \sqrt{3}$
R=r·2=$2 \sqrt{3}$·2=$4 \sqrt{3}$