Answer:
1. [tex]2\frac{5}{8}[/tex]
Step-by-step explanation:
We can see that CD is angle bisector, So we will use angle bisector theorem which states that the angle bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.
We can set up an equation as:
[tex]\frac{AC}{AD}=\frac{BC}{BD}[/tex]
Upon substituting our given values we will get,
[tex]\frac{3}{AD}=\frac{5}{(7-AD)}}[/tex]
Cross multiplying our equation we will get,
[tex]5AD=3*(7-AD)[/tex]
[tex]5AD=21-3AD[/tex]
[tex]5AD+3AD=21[/tex]
[tex]8AD=21[/tex]
[tex]AD=\frac{21}{8}[/tex]
[tex]AD=2\frac{5}{8}[/tex]
Therefore, the length of AD is [tex]2\frac{5}{8}[/tex] units and 1st option is the correct choice.
