If `k=8sqrt(2) and (1)/(2)k=sqrt(3h)`, what is the value of h?

Answer

To solve the equation \( \frac{1}{2}k = \sqrt{3h} \) given that \( k = 8\sqrt{2} \), we can follow these steps:

### Step 1: Substitute the value of \( k \)
We know that \( k = 8\sqrt{2} \). We can substitute this value into the equation \( \frac{1}{2}k \).

\[ \frac{1}{2}k = \frac{1}{2}(8\sqrt{2}) = 4\sqrt{2} \]

### Step 2: Set up the equation
Now we can set up the equation using the value we found for \( \frac{1}{2}k \):

\[ 4\sqrt{2} = \sqrt{3h} \]

### Step 3: Square both sides
To eliminate the square root, we square both sides of the equation:

\[ (4\sqrt{2})^2 = (\sqrt{3h})^2 \]

This simplifies to:

\[ 16 \cdot 2 = 3h \]

\[ 32 = 3h \]

### Step 4: Solve for \( h \)
Now we can solve for \( h \) by dividing both sides by 3:

\[ h = \frac{32}{3} \]

### Final Answer
The value of \( h \) is

\[ \boxed{\frac{32}{3}} \]