Answer:
CD = 3 -√3
Explanation:
The ratio of leg lengths in a 30°-60°-90° triangle is ...
1 : √3 : 2
The longest leg of ΔABD is 2√3, so we must multiply all of these ratio values by √3 to see the actual lengths of the triangle sides.
AB : BD : AD = 1 : √3 : 2 = √3 : 3 : 2√3
That is ...
AB = √3
BD = 3
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The lengths of the legs in isosceles right triangle ABC are the same, so ...
BC = AB = √3
Then the length of interest is ...
CD = BD -BC
CD = 3 -√3 . . . . . . . a=3, b=-1