8:9:: 64 : ?

Options

A. 121
B. 100
C. 81
D. 144

Explanation

To solve the analogy problem 8:9::64:?, we will follow these steps:

1. **Understand the Ratio**: The given ratio is 8:9, which means for every 8 units of one quantity, there are 9 units of another quantity.

2. **Identify the Relationship**: Notice that the relationship between the first pair (8 and 9) can be expressed as:
- 8 squared equals 64 (8^2 = 64).
- 9 squared equals 81 (9^2 = 81).

3. **Apply the Same Logic**: Now, we need to apply the same logic to the second pair where the first number is 64. We will find the second number by squaring the second number of the first pair (which is 9).

4. **Calculate the Second Number**:
- Since we know that 9 squared equals 81, we can conclude that the second number in the second pair must be 81.

5. **Final Answer**: Therefore, the complete analogy is 8:9::64:81.

So, the answer is 81.