What well Centre in place of the question mark (?) in the following questions?
`(8)/(21)` of 189 = `(?)^2 -: 2`

Options

A. 6
B. 36
C. `sqrt(6)`
D. 12

Answer

To solve the equation \( \frac{8}{21} \times 189 = \frac{(?)^2}{2} \), we will follow these steps:

### Step 1: Calculate \( \frac{8}{21} \times 189 \)
To find the left side of the equation, we first need to calculate \( \frac{8}{21} \) of 189.

\[ \frac{8}{21} \times 189 = \frac{8 \times 189}{21} \]

### Step 2: Simplify \( \frac{189}{21} \)
Now, we simplify \( \frac{189}{21} \):

\[ 189 \div 21 = 9 \]

So, we can rewrite the equation as:

\[ \frac{8 \times 189}{21} = 8 \times 9 = 72 \]

### Step 3: Set up the equation
Now we have:

\[ 72 = \frac{(?)^2}{2} \]

### Step 4: Multiply both sides by 2
To isolate \( (?)^2 \), we multiply both sides of the equation by 2:

\[ 72 \times 2 = (?)^2 \]

\[ 144 = (?)^2 \]

### Step 5: Solve for \( ? \)
Now, we take the square root of both sides to find the value of \( ? \):

\[ ? = \sqrt{144} \]

\[ ? = 12 \quad \text{or} \quad ? = -12 \]

### Final Answer
Thus, the value that will replace the question mark is \( \pm 12 \).

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