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Elina [12.6K]
2 years ago
11

What is the answer to this question out of the options given

Mathematics
1 answer:
Aleksandr [31]2 years ago
7 0

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

<h3>Application</h3>

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

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