Question

Find the value of x and y

Answer 1

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

What does the information want:

• value of x
• value of y

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 find x's value

          ⇒ let's set up a proportion

                 $\frac{A'B}{AB} =\frac{A'C'}{AC} \\\frac{30}{x+30} =\frac{14}{22} \\14(x+30) = 30*22\\14x + 420 = 660\\14x = 240\\x = 17.143$

• let's find y's value

          ⇒ let's set up a proportion

                 $\frac{BC'}{BC} =\frac{A'C'}{AC} \\\frac{y}{y+15} =\frac{14}{22} \\22y=14(y+15)\\22y=14y+210\\8y=210\\y=26.25$

Answer:

• x= 17.143
• y = 26.25

Hope that helps!

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