Answer:
BD = 6
Step-by-step explanation:
Theorem: The altitude to the hypotenuse of a right triangle is the mean proportional between the segments of the hypotenuse.
So, 
BD = 6
See how easy that is IF you know the theorem.
Answer:
6 units
Step-by-step explanation:
I will just assume that you made a typo when typing the question when saying AB is 6√3. Here is the solution if AB = 6√2.
Since it is given that ABC is a right triangle and x labels each of the legs, the triangle is a right isoceles triangle.
Now we can use the right isoceles triangle theorem to solve the problem. This theorem states that if a leg is "x" in a right isoceles triangle, then the hypotenuse is equal to x√2.
Here, the hypotenuse is equal to 6√2. To figure out the legs, you need to solve the equation 6√2 = x√2. It is solved here:
6√2 = x√2 (Divide by √2)
x = 6
The length of the legs are 6 units.
1/2 times 1/2 is your answer, because all the diagrams represent that
