Question

ajuor va rog frumos ​

Answer 1

Răspuns:

Știm că în Δ echilateral avem: R= l√3/3; a₃= l√3/6; h=l√3/2; A= l²√3/4

a) R=4√3= l√3/3⇒ l=4√3·3/√3⇒ l=12 cm

a₃= 12√3/6=2√3 cm

h=12√3/2=6√3 cm

A= 12²√3/4=144√3/4=36√3 cm²

b) l=6√3 cm

R= 6√3·√3/3=6·3/3=6 cm

a₃= 6√3·√3/6=3 cm

h= 6√3·√3/2=3·3=9 cm

A= (6√3)²·√3/4=108√3/4=27√3 cm²

c) a₃= 2√6 cm=l√3/6⇒ l = 2√6·6/√3=12√2 cm

R= 12√2·√3/3=4√6 cm

h= 12√2·√3/2=6√6 cm

A= (12√2)²·√3/4=288·√3/4=72√3 cm²

d) h=9√2 cm= l√3/2⇒ l= 9√2·2/√3=18√6/3=6√6 cm

R= 6√6·√3/3=2√18=2·3√2=6√2 cm

a= 6√6·√3/6=√18=3√2 cm

A=(6√6)²·√3/4=36·6·√3/4=9·6·√3=54√3 cm²

e) A= 108√3 cm²= l²√3/4⇒ l²=108√3·4/√3=108·4=432⇒ l=12√3 cm

R= 12√3·√3/3=12 cm

a= 12√3·√3/6=12·3/6=6 cm

h=12√3·√3/2=6·3=18 cm

Explicație pas cu pas: