Question

If \( m = 5 \) and \( n = m + 7 \), then the value of \( \sqrt{m^2 + n^2} \) will be:

• A. 65
• B. 26
• C. 13
• D. 17

Hint:

When finding the value of \( \sqrt{m^2 + n^2} \), substitute the values of \( m \) and \( n \), and simplify the expression.

Answer 1

The Correct Option is D

Step 1: Substitute the values of \( m \) and \( n \).
We are given that \( m = 5 \) and \( n = m + 7 \). Therefore, \[ n = 5 + 7 = 12. \]
Step 2: Apply the formula.
We need to find the value of \( \sqrt{m^2 + n^2} \). Substituting \( m = 5 \) and \( n = 12 \), we get: \[ \sqrt{m^2 + n^2} = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169}. \]
Step 3: Solve the square root.
\[ \sqrt{169} = 13. \]
Step 4: Conclusion.
Therefore, the value of \( \sqrt{m^2 + n^2} \) is 13.