Explanation:

To solve the problem, we understand that 256, K, K, and 81 are in proportion. This means the ratio of the first two terms is equal to the ratio of the last two terms.

- The proportion can be written as: 256/K = K/81.

- By cross-multiplying, we get: 256 * 81 = K * K.

- Simplifying, K² = 20736.

- Taking the positive square root (since K is positive), K = 144.

Now, let's look at the options:

- Option 1: 126

- Option 2: 156

- Option 3: 144

- Option 4: 164

The correct value of K is 144.

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