Answer:
AE = 4
Step-by-step explanation:
Use the formula
AE*EC = DE*EB
Since we don't know AE or EC, let AE = x and then EC will = 16 - x. The formula then becomes
x(16 - x) = 8(6)
[tex]16x-x^2=48[/tex]
Getting everything on one side and setting it equal to 0 will allow us to factor for x:
[tex]x^2-16x+48=0[/tex]
Factoring that gives you that
x = 4 and x = 12. That means that one of those sements has a length of 4 and the other has a length of 12. AE is shorter so it's 4 and EC = 12
