Every two triangles are similar. Therefore the sides of triangles are in proportion.
We have the equations:
1.
[tex]\dfrac{3}{5}=\dfrac{3+x}{20}[/tex] cross multiply
[tex]5(3+x)=(3)(20)[/tex] divide both sides by 5
[tex]3+x=(3)(4)[/tex]
[tex]3+x=12[/tex] subtract 3 from both sides
[tex]\boxed{x=9}[/tex]
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2.
[tex]\dfrac{3}{4}=\dfrac{9}{y}[/tex] cross multiply
[tex]3y=(4)(9)[/tex]
[tex]3y=36[/tex] divide both sides by 3
[tex]\boxed{y=12}[/tex]
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3.
[tex]\dfrac{3}{5}=\dfrac{3+9+u}{60}[/tex]
[tex]\dfrac{3}{5}=\dfrac{12+u}{60}[/tex] cross multiply
[tex]5(12+u)=(3)(60)[/tex] divide both sides by 5
[tex]12+u=(3)(12)[/tex]
[tex]12+u=36[/tex] subtract 12 from both sides
[tex]\boxed{u=24}[/tex]
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4.
[tex]\dfrac{3}{4}=\dfrac{24}{v}[/tex] cross multiply
[tex]3v=(4)(24)[/tex]
[tex]3v=96[/tex] divide both sides by 3
[tex]\boxed{v=32}[/tex]
