$\dfrac{a}{4}=\dfrac{b}{3}$ và $\dfrac{b}{2}=\dfrac{c}{5}$
$→\dfrac{a}{8}=\dfrac{b}{6}=\dfrac{c}{15}$
$→\dfrac{a^2}{64}=\dfrac{b^2}{36}=\dfrac{c^2}{225}$
Áp dụng tính chất dãy tỉ số bằng nhau:
$\dfrac{a^2}{64}=\dfrac{b^2}{36}=\dfrac{c^2}{225}=\dfrac{a^2+b^2+c^2}{64+36+225}=\dfrac{325}{325}=1$
$→\begin{cases}\dfrac{a^2}{64}=1\\\dfrac{b^2}{36}=1\\\dfrac{c^2}{225}=1\end{cases}$
$→\begin{cases}a^2=64\\b^2=36\\c^2=225\end{cases}$
\(\left[ \begin{array}{l}a=8\\a=-8\end{array} \right.\)
\(\left[ \begin{array}{l}b=6\\b=-6\end{array} \right.\)
\(\left[ \begin{array}{l}c=15\\c=-15\end{array} \right.\)
mà $a,b,c>0$
$→\begin{cases}a=8\\b=6\\c=15\end{cases}$
Vậy $(a;b;c)=(8;6;15)$
