Answer:
(c) (28/3)√6
Step-by-step explanation:
Side ratios of "special triangles" are used to solve this problem.
30-60-90° triangle — 1 : √3 : 2
45-45-90° triangle — 1 : 1 : √2
Application
We need to apply these ratios a few times:
CD : CE = √3 : 2 ⇒ CE = (7√3)(2/√3) = 14
CE : BE = 1 : √2 ⇒ BE = 14(√2) = 14√2
BE : AE = √3 : 2 ⇒ AE = (14√2)(2/√3) = (28√2)/√3
The fraction can be simplified by multiplying by (√3)/(√3):
((28√2)/√3)×(√3)/(√3) = (28√6)/3
AE = (28/3)√6
