The perimeter of triangle ABC is 29 meters. Line segment AD bisects angle A. Find AB and AC. CD=5cm, DB=4 cm.(triangle angle bisector theorem)

AB/AC = 4/5 so AB = 4 AC/5

AB + AC + 9 = 29
so
AB + AC = 20

4 AC/5 + AC = 20
4 AC + 5 AC = 100
9 AC = 100
etc

AC= 11.11111111

AB= 8.888888889

You forgot to change 29m to 2900cm.

*The problem should say 29 cm.

AB/AC=4/5, so 4AC=5AB, which is also 4/5(AC)=AB.

AB+BC+AC=29
AB+AC+9=29
AB+AC=20
4/5(AC)+AC=20
9/5(AC)=20
AC=11 1/9

AB=20-AC
AB=20-11 1/9
AB=8 8/9

To find the lengths of AB and AC, we can use the triangle angle bisector theorem. According to this theorem, the ratio of the lengths of the sides of a triangle is equal to the ratio of the lengths of the corresponding angle bisectors.

In triangle ABC, we have AD as the angle bisector of angle A. So, we can let x be the length of AB and y be the length of AC.

Using the triangle angle bisector theorem, we can set up the following proportion:

AB / AC = BD / CD

Substituting the given values, we have:

x / y = 4 / 5

Now, to find the actual values of AB and AC, we need more information. Given that the perimeter of triangle ABC is 29 meters, we can set up another equation using the fact that the sum of the lengths of the sides of a triangle is equal to its perimeter.

AB + AC + BC = 29

Substituting the variables, we have:

x + y + BC = 29

Since we don't have information about BC, we cannot find the exact values of AB and AC. We can only express them in terms of BC.

So, the answer would be:
AB = 4x / (4 + 5)
AC = 5x / (4 + 5)

To find the actual values of AB and AC, we would need to know the length of BC or have additional information about the triangle.