If `(64)^2 - (36)^2 = 20 k` then the value of k is :

Options

A. 140
B. 120
C. 80
D. none of these

Answer

To solve the equation \( (64)^2 - (36)^2 = 20k \), we can use the difference of squares formula, which states that:

\[ A^2 - B^2 = (A - B)(A + B) \]

In our case, \( A = 64 \) and \( B = 36 \).

### Step 1: Apply the difference of squares formula
Using the formula, we can rewrite the left-hand side:

\[ (64)^2 - (36)^2 = (64 - 36)(64 + 36) \]

### Step 2: Calculate \( 64 - 36 \) and \( 64 + 36 \)
Now, we calculate the two expressions:

\[ 64 - 36 = 28 \]
\[ 64 + 36 = 100 \]

### Step 3: Substitute back into the equation
Now we substitute these values back into the equation:

\[ (64)^2 - (36)^2 = (28)(100) \]

### Step 4: Calculate \( 28 \times 100 \)
Now we calculate \( 28 \times 100 \):

\[ 28 \times 100 = 2800 \]

### Step 5: Set the equation equal to \( 20k \)
Now we have:

\[ 2800 = 20k \]

### Step 6: Solve for \( k \)
To find \( k \), we divide both sides by 20:

\[ k = \frac{2800}{20} \]

### Step 7: Calculate \( \frac{2800}{20} \)
Now we perform the division:

\[ k = 140 \]

### Final Answer
Thus, the value of \( k \) is:

\[ \boxed{140} \]

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