2 years ago

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

Mathematics

1 answer:

Aleksandr [31]2 years ago

7 0

Answer:

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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