Final answer:
The Angle Bisector Theorem is used to solve this problem. By setting up an equation using the theorem and the known lengths of the triangle's sides, it is found that the lengths of BD and DC are 3 cm and 4.2 cm respectively.
Step-by-step explanation:
In the given scenario, we can use the Angle Bisector Theorem. The Angle Bisector Theorem states that the ratio of the lengths of the two segments created by the angle bisector is equal to the ratio of the lengths of the two other sides of the triangle.
This translates into: AB/AC = BD/DC.
If you substitute the known lengths, you'll get the equation: 10/14 = BD/DC.
In order to solve this equation, you first need to simplify the ratio 10/14 to 5/7.
Then, you can express BD and DC as: BD = 5x and DC = 7x.
This is based on the ratio from the Angle Bisector Theorem.
Substitute these into the equation for side BC (BC = BD + DC) to get: 6 = 5x + 7x.
Solve for x to find that x equals 0.6.
Now, substitute x into the equations for BD and DC. This results in BD = 3 cm and DC = 4.2 cm.
Therefore, the lengths of BD and DC are 3 cm and 4.2 cm respectively.
Learn more about Angle Bisector Theorem