Question

solve similar triangles (advanced)

Answer 1

Answer:

Step-by-step explanation:

The two triangles given that are similar are

EDA and CBA

From this one fact, we get the following proportion.

ED/CB = (x + 8) / x                 Substitute for the line lengths

13/7 = (x + 8)/x                        Cross Multiply

13x = 7(x + 8)                           Remove the brackets

13x = 7x + 56                          Subtract 7x from both sides

13x - 7x = 56

6x = 56                                   Divide both sides by 6

x = 56/6

x = 9.33

Answer 2

Answer:

  x = 9 1/3

Step-by-step explanation:

If we draw line CG that is parallel to AD so it intersects DE at G, it will divide segment DE into DG = 7 units and GE = 6 units. The resulting triangle CGE is similar to triangle ABC. Of course, CG = BD = 8.

  AB/CG = CG/GE

  x/7 = 8/6

  x = 7(8/6) = 7(4/3) = 28/3 . . . . multiply by 7 and reduce the fraction

  x = 9 1/3