Can someone help? Will mark Brainliest

Mathematics

2 answers:

jarptica [38.1K]3 years ago

8 0

Answer: The answer is the 3rd one

Step-by-step explanation:

VARVARA [1.3K]3 years ago

6 0

9514 1404 393

Answer:

(d) AE = (32√6)/3

Step-by-step explanation:

The side length ratios in a 30-60-90 triangle are 1 : √3 : 2. In a 45-45-90 triangle, they are 1 : 1 : √2.

So, we have the side length ratios ...

CE : CD = 2 : √3

BE : CE = √2 : 1

AE : BE = 2 : √3

Then the ratio AE : CE is ...

$\dfrac{AE}{CD}=\dfrac{2}{\sqrt{3}}\cdot\dfrac{\sqrt{2}}{1}\cdot\dfrac{2}{\sqrt{3}}=\dfrac{4\sqrt{2}}{3}$

Multiplying by the length of CD, we have ...

AE = (8√3)(4√2)/3

AE = (32√6)/3 . . . . . matches the last choice

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