The sum of the squares of two numbers is 386. If one of the number is 5, the other will be :

Options

A. 18
B. 19
C. 15
D. 20

Answer

To solve the problem step by step, we need to find the second number when the sum of the squares of two numbers is given as 386, and one of the numbers is 5.

### Step-by-Step Solution:

1. **Identify the given information:**
- One number is \(5\).
- The sum of the squares of the two numbers is \(386\).

2. **Set up the equation:**
- Let the second number be \(x\).
- According to the problem, we can write the equation as:
\[ 5^2 + x^2 = 386 \]

3. **Calculate the square of 5:**
- Calculate \(5^2\):
\[ 5^2 = 25 \]
- Substitute this value back into the equation:
\[ 25 + x^2 = 386 \]

4. **Isolate \(x^2\):**
- To find \(x^2\), subtract \(25\) from both sides:
\[ x^2 = 386 - 25 \]
- Calculate the right side:
\[ x^2 = 361 \]

5. **Take the square root of both sides:**
- To find \(x\), take the square root of \(361\):
\[ x = \sqrt{361} \]
- Calculate the square root:
\[ x = 19 \]

6. **Conclusion:**
- Therefore, the other number is \(19\).

### Final Answer:
The other number will be \(19\).

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