`[(7)^2-(6)^2]div26=18div?`

Options

A. 18
B. 36
C. 9
D. 40

Answer

To solve the equation \(\frac{(7)^2 - (6)^2}{26} = \frac{18}{?}\), we can follow these steps:

### Step 1: Calculate \(7^2\) and \(6^2\)
First, we need to find the squares of 7 and 6:
\[ 7^2 = 49 \]
\[ 6^2 = 36 \]

### Step 2: Subtract the squares
Now, we subtract \(6^2\) from \(7^2\):
\[ 49 - 36 = 13 \]

### Step 3: Set up the equation
Now we can rewrite the equation using the results from the previous steps:
\[ \frac{13}{26} = \frac{18}{x} \]

### Step 4: Simplify the left side
Next, we simplify the left side of the equation:
\[ \frac{13}{26} = \frac{1}{2} \]
So, we have:
\[ \frac{1}{2} = \frac{18}{x} \]

### Step 5: Cross-multiply to solve for \(x\)
Now, we can cross-multiply to find \(x\):
\[ 1 \cdot x = 2 \cdot 18 \]
This simplifies to:
\[ x = 36 \]

### Conclusion
Thus, the value of the question mark is:
\[ \boxed{36} \]