Question

Determina lungimile laturilor triunghiului ABC stiind ca :
perimetrul triunghiului ABC = 17 cm , 4×AB = 5×AC si BC = AC .
DAU COROANA ! VA ROG AJUTATI - MA ! SUNT DISPERATA !

Answer 1

AB+AC+BC =17 CM
4AB =5AC  ;     AB =5AC/4
BC=AC

5AC/4 + AC +AC = 17
5AC+4AC+4AC =68
13AC =68
AC =5.23 cm
BC =AC =5.23
AB =5AC/4 =5*5.23 /4 =6.54 cm

Answer 2

   
[tex]\displaystyle \bf\\ \begin{cases} \bf BC=AC\\ \bf AB+AC+BC=17\\ \bf 4AB=5AC\\ \end{cases}\\\\ \begin{cases} \bf AB+2AC=17~\Longrightarrow~ AB=17-2AC~\text{\bf(substitutie)}\\ \bf 4AB-5AC=0\\ \end{cases}\\\\ 4(17-2AC)-5AC=0\\ 68-8AC-5AC=0\\ 68-13AC=0\\ 13AC=68\\ AC=\boxed{\bf\frac{68}{13}}\\ BC=AC=\boxed{\bf\frac{68}{13}}\\ AB=17-2AC=17-2\times\frac{68}{13}=\frac{17\times13}{13}-\frac{2\times68}{13}=\\\\ =\frac{221}{13}-\frac{136}{13}=\boxed{\bf\frac{85}{13}}[/tex]


[tex]\displaystyle \bf \\ \text{\bf Verificare:}\\\\ AC + BC + AB = \frac{68}{13} + \frac{68}{13} +\frac{85}{13} =\frac{68+68+85}{13}=\frac{221}{13} = \boxed{\bf 17} [/tex]