Question

Given $dc = 7$, $cb = 8$, $ab = \frac{1}{4}ad$, and $ed = \frac{4}{5}ad$, find $fc$. Express your answer as a decimal.

Answer 1

A ↔ B ↔ C ↔ D ↔ E ↔ F

 $\frac{1}{4} AD$      8      7      $\frac{4}{5} AD$   ???

AB + BC + CD = AD   segment addition postulate

$\frac{1}{4} AD$   +   8   +   7   = AD

$\frac{1}{4} AD$   +       15        = AD

AD         + 60    = 4AD

                  60    = 3AD

                  20    = AD

AB =  $\frac{1}{4} AD$    =  $\frac{1}{4}(20)$    = 5

DE =  $\frac{4}{5}AD$   =  $\frac{4}{5}(5)$    = 4

CD + DE + EF = CF   segment addition postulate

7   +   4   + EF  = CF

     11        + EF  = CF

Answer: 11 + EF

Note: You did not provide any info about EF.  If you have additional information that you did not type in, calculate EF and add it to 11 to find the length of CF.

Answer 2

The answer is 11+EF I checked it