Answer:
BD = 13
Step-by-step explanation:
AC is an angle bisector and divides the opposite into segments that are proportional to the other 2 sides, that is
[tex]\frac{AB}{AD}[/tex] = [tex]\frac{BC}{DC}[/tex] , substitute values
[tex]\frac{12}{27}[/tex] = [tex]\frac{x}{x+5}[/tex] ( cross- multiply )
27x = 12(x + 5)
27x = 12x + 60 ( subtract 12x from both sides )
15x = 60 ( divide both sides by 15 )
x = 4
Thus
BD = x + x + 5 = 2x + 5 = 2(4) + 5 = 8 + 5 = 13
