Question

If AC = 3, BC = 5, and AB = 7, find AD: 2 5/8 4 1/5 4 3/8 11 2/3

Answer 1

Answer:

1.  $2\frac{5}{8}$  

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:  

$\frac{AC}{AD}=\frac{BC}{BD}$

Upon substituting our given values we will get,

$\frac{3}{AD}=\frac{5}{(7-AD)}}$

Cross multiplying our equation we will get,

$5AD=3*(7-AD)$

$5AD=21-3AD$

$5AD+3AD=21$

$8AD=21$

$AD=\frac{21}{8}$

$AD=2\frac{5}{8}$

Therefore, the length of AD is $2\frac{5}{8}$ units and 1st option is the correct choice.