Answer:
DE=9
FE=15
Step-by-step explanation:
Triangle EBC is similar to triangle EDF.
Therefore
[tex] \frac{DE}{DB}= \frac{FE}{CE}[/tex]
[tex] \frac{5x - 4 + 3}{3} = \frac{4x + 2 + 5}{5} [/tex]
[tex] \frac{5x - 1}{3} = \frac{4x + 7}{5} [/tex]
[tex]5(5x - 1) = 3(4x + 7)[/tex]
Expand to get;
[tex]25x - 5 = 12x + 21[/tex]
Group similar terms:
[tex]25x - 12x = 21 + 5[/tex]
[tex]13x = 26[/tex]
Divide both sides by 13 to get:
[tex]x = 2[/tex]
We substitute to get:
DE= 5x-3+4
DE=5*2-3+4
DE=10-1=9
Also,
FE=4x+2+5
FE =4*2+2+5
FE=8+7
FE=15
