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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