Question

What is the length of segment AE?

(3 points – 1 point correct formula(s), 1 point correct proportion(s), 1 point accurate calculations)

Answer 1

`(50)/(3)`

Explanation:

∵BC // DE

∴m∠DEC=m∠BCA

∵m∠B=m∠D=90°

∴m∠DCE=m∠BAC

∴ΔCDE similar to ΔABC

∴
`(AB)/(CD)=(BC)/(DE)  \\(6)/(4)=(8)/(DE)`

∴DE=16/3

`AC=\sqrt{6^(2)+8^(2)  } =10`

`CE=\sqrt{4^(2)+((16)/(3)) ^(2)   } =(20)/(3)`

`AE=10+(20)/(3) =(50)/(3)`