violet7963
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ABC and DEF are similar triangles. If the side lengths of ABC are 6, 8, and 12, and the
longest side of DEF is 18, then what are its other side lengths?
9 and 14
9 and 12
14 and 16
24 and 36

Respuesta :

akposevictor

Applying the properties of similar triangles, the other side lengths of ΔDEF are: B. 9 and 12

Properties of Similar Triangles:

  • The ratio of the corresponding sides two triangles that are similar to each other are the same/equal.

Given that ΔABC and ΔDEF are similar triangles, therefore:

  • Let, a = 6, b = 8, and c = 12 be the sides of ΔABC.
  • Let, x, y, and z be the sides of ΔDEF.
  • Let z = 18

Thus:

a/x = b/y = c/z

  • Substitute

6/x = 8/y = 12/18

Find x using 6/x = 12/18:

6/x = 12/18

  • Cross multiply

x = [tex]\frac{18 \times 6}{12}[/tex]

x = 9

Find x using 8/y = 12/18:

8/y = 12/18

  • Cross multiply

x = [tex]\frac{18 \times 8}{12}[/tex]

x = 12

Therefore, applying the properties of similar triangles, the other side lengths of ΔDEF are: B. 9 and 12

Learn more about similar triangles on:

https://brainly.com/question/11899908

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