\(\begin{array}{l}
\dfrac{2}{3}x = \dfrac{3}{4}y = \dfrac{4}{5}z\\
\Leftrightarrow \dfrac{{2x}}{3} = \dfrac{{3y}}{4} = \dfrac{{4z}}{5}\\
\Leftrightarrow \dfrac{{2x}}{{3.12}} = \dfrac{{3y}}{{4.12}} = \dfrac{{4z}}{{5.12}}\\
\Leftrightarrow \dfrac{x}{{18}} = \dfrac{y}{{16}} = \dfrac{z}{{15}} = \dfrac{{x + y + z}}{{49}} = \dfrac{{196}}{{49}} = 4\\
\Rightarrow x = 18.4 = 72\\
y = 16.4 = 64\\
z = 15.4 = 60\\
b)\,\dfrac{x}{2} = \dfrac{y}{3} = \dfrac{z}{4} \Rightarrow \dfrac{{{x^2}}}{4} = \dfrac{{{y^2}}}{9} = \dfrac{{{z^2}}}{{16}} = \dfrac{{{x^2} + {y^2} + {z^2}}}{{4 + 9 + 16}} = \dfrac{{29}}{{29}} = 1\\
\Rightarrow {x^2} = 4 \Rightarrow x = \pm 2\\
{y^2} = 9 \Rightarrow y = \pm 3\\
{z^2} = 16 \Rightarrow z = \pm 4
\end{array}\)
