Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
What does the information want:
Let's gather some information:
- ΔA'BC' and ΔABC are similar triangles
⇒ Angle B is shared by both triangles
⇒ Angle A' and A are the same, as they are both on parallel
lines, A'C' and AC, and both angles are formed with the
same line AB
⇒ by the Angle-Angle Theorem*, they are similar triangles
If they are similar triangles:
⇒ their side lengths are proportional to each other
⇒ let's set up a proportion
[tex]\frac{A'B}{AB} =\frac{A'C'}{AC} \\\frac{30}{x+30} =\frac{14}{22} \\14(x+30) = 30*22\\14x + 420 = 660\\14x = 240\\x = 17.143[/tex]
⇒ let's set up a proportion
[tex]\frac{BC'}{BC} =\frac{A'C'}{AC} \\\frac{y}{y+15} =\frac{14}{22} \\22y=14(y+15)\\22y=14y+210\\8y=210\\y=26.25[/tex]
Answer:
Hope that helps!
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