Question

1) Mediile aritmetice ale laturilor unui triunghi luate doua cate doua sunt 2,7 cm; 2,15 cm si 2,6 cm. Calculati perimetrul triunghiului si lungimile celor trei laturi.
AJUTOR URGENT!!!!!!!!!!!!!!

Answer 1

   
[tex]\displaystyle a,~b,~c ~~ \text{sunt laturile triunghiului. } \\ \\ \frac{a+b}{2}=2,7\;cm~~~\Longrightarrow ~~~ a+b=2,7\times 2 = 5,4 cm \\ \\ \frac{b+c}{2}=2,15\;cm~~~\Longrightarrow ~~~ b+c=2,15\times 2 = 4,3 cm \\ \\ \frac{c+a}{2}=2,6\;cm~~~\Longrightarrow ~~~ c+a=2,6\times 2 = 5,2 cm \\ \\ \text{Scriem ecuatiile: } \\ a+b~~~~~=5,4 \\ ~~~~~~b+c=4,5 \\ a~~~~\;+c=5,2 ~~~~~| \times (-1)\\ \text{--------------------------} \\ [/tex]

[tex]\displaystyle ~~~a+b~~~~~=5,4 \\ ~~~~~~~~~b+c=4,3 \\ -a~~~~\;-c=-5,2 \\ \text{-------------------------- adunam ecuatiile} \\ 2b = 5,4+4,3-5,2 \\ 2b = 4,5 \\ \\ b= \frac{4,4}{2} = \boxed{ 2,25\;cm} \\ a = 5,4-b=5,4-2,25=\boxed{3,15\;cm} \\ c=5,2 - a = 5,2-3,15=\boxed{2,05\;cm} \\ \\ P = a+b+c = 2,25+3,15+2,05 = \boxed{7,45\;cm}[/tex]