Answer:
15
Step-by-step explanation:
∆ABC ~ ∆AED, therefore,
[tex] \frac{AB}{AE} = \frac{BC}{ED} [/tex]
Let BE = x
AB = x + 9
AE = 9
BC = 16
ED = 6
Plug in the values into the equation
[tex] \frac{x + 9}{9} = \frac{16}{6} [/tex]
[tex] \frac{x + 9}{9} = \frac{8}{3} [/tex]
Cross multiply
[tex] (x + 9)(3) = (8)(9) [/tex]
[tex] 3x + 27 = 72 [/tex]
Subtract 27 from each side
[tex] 3x = 72 - 27 [/tex]
[tex] 3x = 45 [/tex]
Divide both sides by 3
[tex] x = \frac{45}{3} [/tex]
[tex] x = 15 [/tex]
Segment BE = x = 15
