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STatiana [176]
2 years ago
13

Find the value of x and y

Mathematics
1 answer:
Natalija [7]2 years ago
5 0

Hello and Good Morning/Afternoon:

<u>Let's take this problem step-by-step</u>:

<u>What does the information want:</u>

  • value of x
  • value of y

<u>Let's gather some information</u>:

  • 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 <em>Angle-Angle Theorem*</em>, they are similar triangles

<u>If they are similar triangles</u>:

   ⇒ 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

<u>Answer:</u>

  • <u>x= 17.143</u>
  • <u>y = 26.25</u>

Hope that helps!

#LearnwithBrainly

 

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