Find the value of (?) in following approximation questions :
`?% "of 179.99" = sqrt((24.02)^(2) +(17.98)^(2) + 60.01% "of 659.98")`

Options

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

Answer

To solve the given approximation question step by step, we will follow the calculations as described in the video transcript.

### Step 1: Set up the equation
We start with the equation:
\[ ? \% \text{ of } 179.99 = \sqrt{(24.02)^2 + (17.98)^2 + 60.01\% \text{ of } 659.98} \]

### Step 2: Approximate the values
We will approximate the numbers for easier calculations:
- Approximate \(179.99\) to \(180\)
- Approximate \(24.02\) to \(24\)
- Approximate \(17.98\) to \(18\)
- Approximate \(60.01\%\) to \(60\%\)
- Approximate \(659.98\) to \(660\)

Thus, the equation becomes:
\[ ? \% \text{ of } 180 = \sqrt{(24)^2 + (18)^2 + 60\% \text{ of } 660} \]

### Step 3: Calculate the squares
Now, we calculate the squares:
- \((24)^2 = 576\)
- \((18)^2 = 324\)

### Step 4: Calculate \(60\%\) of \(660\)
Next, we calculate \(60\%\) of \(660\):
\[ 60\% \text{ of } 660 = \frac{60}{100} \times 660 = 396 \]

### Step 5: Substitute and simplify
Now we substitute these values back into the equation:
\[ ? \% \text{ of } 180 = \sqrt{576 + 324 + 396} \]

### Step 6: Add the values inside the square root
Now we add the values:
\[ 576 + 324 + 396 = 1296 \]

### Step 7: Calculate the square root
Now we find the square root:
\[ \sqrt{1296} = 36 \]

### Step 8: Set up the percentage equation
Now we have:
\[ ? \% \text{ of } 180 = 36 \]
This can be rewritten as:
\[ \frac{?}{100} \times 180 = 36 \]

### Step 9: Solve for \(?\)
To find \(?\), we rearrange the equation:
\[ ? = \frac{36 \times 100}{180} \]

### Step 10: Simplify the fraction
Now we simplify:
\[ ? = \frac{3600}{180} = 20 \]

### Final Answer
Thus, the value of \(?\) is:
\[ \boxed{20} \]