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

Guest Jan 30, 2019

#1**+1 **

We have that

AD = DC + CB + AB

AD = 7 + 8 + (1/4)AD

(3/4)AD = 15

AD = 15 * (4/3) = 20

So ED = (4/5)AD = (4/5)(20) = 16

Note that CA = CB + AB = 8 + (1/4)AD = 8 + (1/4)16 = 8 + 4 = 12

So....by similar triangles

ED /AD = FC /CA

16 / 20 = FC / 12

4 /5 = FC /12 multiply both sides by 12

12 * 4 /5 = FC = 48 / 5 = 9.6

CPhill Jan 30, 2019