Question 1202110
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https://drive.google.com/file/d/1zsj-S2V9xnu6WYPC88f8xYPvpK_pVFyO/view?usp=sharing
What is the value of x?
Use the rules of special right triangles to find x.
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            The solution and the answer in the post by @mananth are  FATALLY  WRONG.

            I came to bring a correct solution.



<pre>
Triangle ABC is a right-angled isosceles triangle.

It has acute angle of 45°;  hence, the other acute angle is 45°, too,
and the triangle ABC is isosceles.


Its hypotenuse has the length of  {{{6*sqrt(2)}}}  units.

Hence, both its legs, AB and BC, have the same length of  {{{(6*sqrt(2))/sqrt(2)}}} = 6 units.



Triangle BCD is a right-angled triangle.

Its acute angle BCD  has the measure of 90° - 60° = 30°.

Its hypotenuse BC is 6 units long, as we found it above.


Hence, x = BD has the length half of the hypotenuse BC, i.e. 6/2 = 3 units,
as the leg opposite to the angle of 30°.



<U>ANSWER</U>.  x is 3 units long.  x = 3.
</pre>

Solved.