If A% of A is 196, then what is the value of A?

Options

A. 170
B. 160
C. 120
D. 140

Answer

To solve the problem "If A% of A is 196, then what is the value of A?", we can follow these steps:

### Step 1: Understand the expression
The expression "A% of A" can be mathematically represented as:
\[ \frac{A}{100} \times A \]
This simplifies to:
\[ \frac{A^2}{100} \]

### Step 2: Set up the equation
According to the problem, we know that:
\[ \frac{A^2}{100} = 196 \]

### Step 3: Eliminate the fraction
To eliminate the fraction, multiply both sides of the equation by 100:
\[ A^2 = 196 \times 100 \]
Calculating the right side gives:
\[ A^2 = 19600 \]

### Step 4: Solve for A
Now, take the square root of both sides to find A:
\[ A = \sqrt{19600} \]
Calculating the square root gives:
\[ A = 140 \]

### Step 5: Conclusion
Thus, the value of A is:
\[ \boxed{140} \]