Respuesta :

Answer:

  • x = 4√6 or 9.8

Step-by-step explanation:

The two smaller triangles are similar.

The ratio of corresponding sides of similar triangles is equal:

  • 12/x = x/8
  • x² = 12*8
  • x² = 96
  • x = √96
  • x = 4√6 or 9.8
  • x is the angle bisector of a right angle . Applying Thales theorem

[tex]\\ \sf\longmapsto x^2=12(8)[/tex]

[tex]\\ \sf\longmapsto x^2=96[/tex]

[tex]\\ \sf\longmapsto x=\sqrt{96}[/tex]

[tex]\\ \sf\longmapsto x=9.7[/tex]

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