Respuesta :

suspho

DB : EA = DC : EC

10 : x = 9 : (9 + 6)

10 : x = 9 : 15

x = (10 * 15) : 9

x = 150 : 9

x = 16.66

16.66 cm is your answer

akposevictor

By applying the theorem of similar triangles and their side ratio, the length of EA is approximately: 16.7 cm

Triangle CDB and triangle CEA are similar triangles.

Based on the theorem of similar triangles, the ratio of the side lengths of triangle CDB to the corresponding side lengths of triangle CEA would be equal.

Given:

  • CD = 9 cm
  • CE = 9 + 6 = 15 cm
  • DB = 10 cm

  • Thus:

EA/DB = CE/CD

  • Substitute

[tex]\frac{EA}{10} = \frac{15}{9} \\[/tex]

  • Cross multiply

[tex]EA \times 9 = 10 \times 15\\\\EA \times 9 = 150[/tex]

  • Divide both sides by 9

EA = 16.6 cm

Therefore, by applying the theorem of similar triangles and their side ratio, the length of EA is approximately: 16.7 cm

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