What is BD? In triangle ABC, the length of side AB is 12 and the length of side AD is 27. The line AC started from point A and cuts the side BD a point C. The length of BC is x and the length of CD is x + 5.

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answer: the proof is mentioned below.

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since, given:   lines bc = ef

prove:   lines ac > ef

          statements                                           reason

1. bc=ef                                           1. given

2. ac= ab+bc                                 2. because b is the point between the  

                                                            line segment ac

3.   ac > bc                                       3. because if a line segment is equal to

                                                          the sum of two line segments then it is

                                                          always greater then each of these

                                                          individual line segments

4. ac > ef                                         4. by equality property.