Respuesta :

Answer:

AB = 3

Step-by-step explanation:

given that BK is an angle bisector then the following ratios are equal

[tex]\frac{AB}{BC}[/tex] = [tex]\frac{AK}{KC}[/tex]

substitute relevant values into the equation and solve for AB

[tex]\frac{AB}{5}[/tex] = [tex]\frac{2.625}{4.375}[/tex] ( cross- multiply )

4.375AB = 13.125 ( divide both sides by 4.375 )

AB = 3


Applying the angle bisector theorem, given that BK is an angle bisector of triangle ABC, thus: AB = 3

Recall:

  • The angle bisector theorem states that when a line bisects an angle of  triangle, the opposite side of the triangle it divides will be proportional to the two other sides of the triangle.

Thus, given that △ABC has an angle bisector, BK, as shown in the diagram attached below, where:

  • BC=5
  • AK=2.625
  • KC=4.375

Therefore:

[tex]\frac{AB}{AK} = \frac{BC}{KC}[/tex]

  • Substitute

[tex]\frac{AB}{2.625} = \frac{5}{4.375}\\\\[/tex]

  • Multiply both sides by 2.625

[tex]AB = \frac{5 \times 2.625}{4.375}\\\\\mathbf{AB = 3}[/tex]

Therefore, applying the angle bisector theorem, given that BK is an angle bisector of triangle ABC, thus: AB = 3

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