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

2 5/8

Explanation:

Answer 2

1.
`2(5)/(8)`

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:

`(AC)/(AD)=(BC)/(BD)`

Upon substituting our given values we will get,

`(3)/(AD)=(5)/((7-AD))}`

Cross multiplying our equation we will get,

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

`5AD=21-3AD`

`5AD+3AD=21`

`8AD=21`

`AD=(21)/(8)`

`AD=2(5)/(8)`

Therefore, the length of AD is
`2(5)/(8)` units and 1st option is the correct choice.