Understanding the Relationship in the Given Set of Numbers

The question asks us to identify the relationship between the numbers in the given set (3, 7, 58) and find another set among the options that follows the same rule. Let's analyze the numbers in the set (3, 7, 58) to discover the underlying pattern or relationship.

We can try various mathematical operations involving the first two numbers to see if we can arrive at the third number.

• Addition: 3 + 7 = 10 (Not 58)
• Subtraction: 7 - 3 = 4 (Not 58)
• Multiplication: 3 × 7 = 21 (Not 58)
• Squares: Let's consider squaring the numbers.

Squaring the first number: $3^2 = 3 \times 3 = 9$

Squaring the second number: $7^2 = 7 \times 7 = 49$

Now, let's see if there's a relationship between the squares and the third number (58). If we add the squares:

$3^2 + 7^2 = 9 + 49 = 58$

This matches the third number in the set (3, 7, 58). So, the relationship is that the third number is the sum of the squares of the first two numbers. We can express this rule as: if the set is (a, b, c), then $a^2 + b^2 = c$.

Applying the Relationship to Find the Matching Set of Numbers

Now, we will test each option to see which set of numbers follows the same relationship ($a^2 + b^2 = c$).

1. Option 1: (7, 5, 39)

   Here, a = 7 and b = 5. We need to check if $7^2 + 5^2$ equals 39.

   $7^2 + 5^2 = (7 \times 7) + (5 \times 5) = 49 + 25 = 74$

   Since 74 ≠ 39, this set does not follow the same relationship.

2. Option 2: (3, 2, 13)

   Here, a = 3 and b = 2. We need to check if $3^2 + 2^2$ equals 13.

   $3^2 + 2^2 = (3 \times 3) + (2 \times 2) = 9 + 4 = 13$

   Since 13 = 13, this set follows the same relationship as the given set of numbers (3, 7, 58).

3. Option 3: (6, 4, 53)

   Here, a = 6 and b = 4. We need to check if $6^2 + 4^2$ equals 53.

   $6^2 + 4^2 = (6 \times 6) + (4 \times 4) = 36 + 16 = 52$

   Since 52 ≠ 53, this set does not follow the same relationship.

4. Option 4: (8, 7, 112)

   Here, a = 8 and b = 7. We need to check if $8^2 + 7^2$ equals 112.

   $8^2 + 7^2 = (8 \times 8) + (7 \times 7) = 64 + 49 = 113$

   Since 113 ≠ 112, this set does not follow the same relationship.

Conclusion: The Set with the Same Number Analogy

After checking all the options, only the set (3, 2, 13) demonstrates the same relationship as the initial set of numbers (3, 7, 58). The relationship is consistent: the sum of the squares of the first two numbers equals the third number.

Therefore, the set that is related in the same way as (3, 7, 58) is (3, 2, 13).