The length and breath of a rectangle are `(6x^(2)-2)` units and `(5x+2)` units respectively. Find its perimeter.

Answer

To find the perimeter of a rectangle given its length and breadth, we can follow these steps:

### Step 1: Identify the length and breadth
The length (l) of the rectangle is given as:
\[ l = 6x^2 - 2 \]
The breadth (b) of the rectangle is given as:
\[ b = 5x + 2 \]

### Step 2: Write the formula for the perimeter
The formula for the perimeter (P) of a rectangle is:
\[ P = 2 \times (l + b) \]

### Step 3: Substitute the values of length and breadth into the formula
Now, we will substitute the values of l and b into the perimeter formula:
\[ P = 2 \times ((6x^2 - 2) + (5x + 2)) \]

### Step 4: Simplify the expression inside the parentheses
Combine the terms inside the parentheses:
\[ P = 2 \times (6x^2 - 2 + 5x + 2) \]
Notice that \(-2\) and \(+2\) cancel each other out:
\[ P = 2 \times (6x^2 + 5x) \]

### Step 5: Distribute the 2
Now, distribute the 2 to both terms inside the parentheses:
\[ P = 2 \times 6x^2 + 2 \times 5x \]
\[ P = 12x^2 + 10x \]

### Final Answer
Thus, the perimeter of the rectangle is:
\[ P = 12x^2 + 10x \]

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