`?% "of" 180.02=sqrt((24.01)^(2)+(18.21)^(2)+60.01% "of" 660.17)`

Options

A. 80
B. 60
C. 40
D. 20

Explanation

To solve the equation \( x\% \text{ of } 180.02 = \sqrt{(24.01)^2 + (18.21)^2 + 60\% \text{ of } 660.17} \), we will follow these steps:

### Step 1: Approximate the values
First, we can approximate the values for easier calculations:
- \( 180.02 \approx 180 \)
- \( 24.01 \approx 24 \)
- \( 18.21 \approx 18 \)
- \( 60\% \text{ of } 660.17 \approx 60\% \text{ of } 660 \)

### Step 2: Calculate \( 60\% \text{ of } 660 \)
To find \( 60\% \text{ of } 660 \):
\[ 60\% \text{ of } 660 = \frac{60}{100} \times 660 = 396 \]

### Step 3: Calculate \( (24)^2 \) and \( (18)^2 \)
Next, we calculate the squares:
\[ (24)^2 = 576 \]
\[ (18)^2 = 324 \]

### Step 4: Add the squares and the percentage
Now, we can add these values:
\[ 576 + 324 + 396 = 1296 \]

### Step 5: Find the square root
Now, we take the square root of the sum:
\[ \sqrt{1296} = 36 \]

### Step 6: Set up the equation
Now we set up the equation:
\[ x\% \text{ of } 180 = 36 \]
This can be written as:
\[ \frac{x}{100} \times 180 = 36 \]

### Step 7: Solve for \( x \)
To find \( x \), we rearrange the equation:
\[ x = \frac{36 \times 100}{180} \]
Simplifying this:
\[ x = \frac{3600}{180} = 20 \]

### Conclusion
Thus, the value of \( x \) is \( 20 \).