Find the value of x. Please help!

x = 3

Step-by-step explanation:

Using the triangle similarity theorem

x/x+3 = x+3/12

Cross multiply

12x = (x+3)(x+3)

12x = x²+3x+3x+9

12x =  x²+6x+9

x²+6x+9-12x = 0

x²-6x+9 = 0

Factorize

x²-3x-3x+9 = 0

x(x-3)-3(x-3) = 0

x - 3 = 0

x = 3 twice

Hence the value of x is 3

answer: the proof is mentioned below.

step-by-step explanation:

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.