Answer:
[tex]x=16\dfrac{28}{37}\\ \\y=5\dfrac{1}{3}\\ \\z=7.5[/tex]
Step-by-step explanation:
The diagram shows three paralel lines which divide the large triangle into three similar triangles.
By Thales theorem,
[tex]\dfrac{5}{z}=\dfrac{y}{8}=\dfrac{2}{3}[/tex]
Then
[tex]\dfrac{5}{z}=\dfrac{2}{3}\Rightarrow 2z=15,\ z=7.5\\ \\\dfrac{y}{8}=\dfrac{2}{3}\Rightarrow 3y=16,\ y=\dfrac{16}{3}=5\dfrac{1}{3}[/tex]
From the similarity of triangles,
[tex]\dfrac{x}{20}=\dfrac{z+8}{z+8+3}\\ \\\dfrac{x}{20}=\dfrac{7.5+8}{7.5+8+3}\\ \\\dfrac{x}{20}=\dfrac{15.5}{18.5}\\ \\x=20\cdot \dfrac{155}{185}=20\cdot \dfrac{31}{37}=\dfrac{620}{37}=16\dfrac{28}{37}[/tex]
