Question

Se stie ca triunghiul ABC~triunghiul A'B'C',Perimetrul triunghiului ABC =27cm,A'B'=10cm,A'C=16cm,B'C'=28cm.
Atunci:
a)AB=.......cm;
b)AC=.......cm;
c)BC=........cm.

Answer 1

$\frac{AB}{ A^{1} B^{1} }$=$\frac{AC}{A^{1} C^{1} }$=$\frac{BC}{ B^{1} C^{1} }$=$\frac{AB+AC+BC}{ A^{1} B^{1} + A^{1} C^{1} + B^{1} C^{1} }$

AB/10=AC/16=BC/28=27/(10+16+28)=27/54=1/2
AB/10=1/2   AB=10*1/2=10/2=5 
AC/16=1/2  AC=16*1/2=16/2=8
BC/28=1/2  BC=14