If 7 * 24 = 25 and 12 * 16 = 20, then what is 16 * 63 equal to?

Correct Option (3)

The given operation '*' follows a specific mathematical pattern where the result is the square root of the sum of the squares of the two numbers. This corresponds to the hypotenuse of a right-angled triangle, also known as the Pythagorean theorem (√(a² + b²)).

• For the first example: 7 * 24 = 25. This is consistent with √(7² + 24²) = √(49 + 576) = √625 = 25.
• For the second example: 12 * 16 = 20. This is consistent with √(12² + 16²) = √(144 + 256) = √400 = 20.

Applying this established pattern to the question 16 * 63:

• 16 * 63 = √(16² + 63²)
• = √(256 + 3969)
• = √4225
• = 65

Therefore, 16 * 63 equals 65.

Incorrect Options:

Options 1 (70), 2 (66), and 4 (64) are incorrect because they do not satisfy the identified mathematical pattern of √(a² + b²) derived from the given examples. These values would not result from applying the Pythagorean theorem to the numbers 16 and 63.