The value of `((75.8)^(2) - (55.8)^(2))/(20)` is

Options

A. 20
B. 40
C. 121.6
D. 131.6

Answer

To solve the expression \(\frac{(75.8)^{2} - (55.8)^{2}}{20}\), we can use the difference of squares formula, which states that \(a^2 - b^2 = (a + b)(a - b)\).

### Step-by-Step Solution:

1. **Identify \(a\) and \(b\)**:
- Let \(a = 75.8\) and \(b = 55.8\).

2. **Apply the difference of squares formula**:
- According to the formula, we can rewrite the expression:
\[ (75.8)^{2} - (55.8)^{2} = (75.8 + 55.8)(75.8 - 55.8) \]

3. **Calculate \(a + b\)**:
- Calculate \(75.8 + 55.8\):
\[ 75.8 + 55.8 = 131.6 \]

4. **Calculate \(a - b\)**:
- Calculate \(75.8 - 55.8\):
\[ 75.8 - 55.8 = 20 \]

5. **Substitute back into the expression**:
- Now substitute these values back into the expression:
\[ (75.8)^{2} - (55.8)^{2} = (131.6)(20) \]

6. **Calculate the product**:
- Now calculate \(131.6 \times 20\):
\[ 131.6 \times 20 = 2632 \]

7. **Divide by 20**:
- Now substitute this back into the original expression:
\[ \frac{2632}{20} \]

8. **Final calculation**:
- Now calculate \(\frac{2632}{20}\):
\[ \frac{2632}{20} = 131.6 \]

### Final Answer:
The value of \(\frac{(75.8)^{2} - (55.8)^{2}}{20}\) is \(131.6\).

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