The difference of the squares of two consecutive even natural numbers is 92. Taking x as the smaller of the two numbers, form an equation in x and hence find the larger of the two.

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the variables
Let \( x \) be the smaller of the two consecutive even natural numbers. Therefore, the larger number can be expressed as \( x + 2 \).

### Step 2: Write the equation based on the problem statement
According to the problem, the difference of the squares of these two numbers is 92. We can write this as:
\[ (x + 2)^2 - x^2 = 92 \]

### Step 3: Expand the left-hand side of the equation
Using the identity \( (a + b)^2 = a^2 + 2ab + b^2 \), we expand \( (x + 2)^2 \):
\[ (x + 2)^2 = x^2 + 4x + 4 \]
Now substituting this back into the equation gives:
\[ (x^2 + 4x + 4) - x^2 = 92 \]

### Step 4: Simplify the equation
The \( x^2 \) terms cancel out:
\[ 4x + 4 = 92 \]

### Step 5: Solve for \( x \)
Subtract 4 from both sides:
\[ 4x = 92 - 4 \]
\[ 4x = 88 \]
Now, divide both sides by 4:
\[ x = \frac{88}{4} = 22 \]

### Step 6: Find the larger number
The larger of the two consecutive even numbers is:
\[ x + 2 = 22 + 2 = 24 \]

### Final Answer
Thus, the larger of the two consecutive even natural numbers is **24**.

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