The length of a rectangle is 4 units less than thrice its breadth. If the breadth is y units, find the rule for finding the perimeter of the rectangle.

Answer

To find the rule for calculating the perimeter of the rectangle given that the length is 4 units less than thrice its breadth, we can follow these steps:

### Step 1: Define the variables
Let the breadth of the rectangle be represented as \( y \) units.

### Step 2: Express the length in terms of breadth
According to the problem, the length \( L \) of the rectangle is 4 units less than thrice its breadth. We can express this relationship mathematically:
\[ L = 3y - 4 \]

### Step 3: Write the formula for the perimeter
The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2 \times (L + W) \]
where \( L \) is the length and \( W \) is the width (breadth).

### Step 4: Substitute the values into the perimeter formula
Substituting the expressions for length and breadth into the perimeter formula:
\[ P = 2 \times ((3y - 4) + y) \]

### Step 5: Simplify the expression
Now, simplify the expression inside the parentheses:
\[ P = 2 \times (3y - 4 + y) = 2 \times (4y - 4) \]

### Step 6: Distribute the 2
Now, distribute the 2:
\[ P = 2 \times 4y - 2 \times 4 = 8y - 8 \]

### Final Rule for the Perimeter
Thus, the rule for finding the perimeter of the rectangle is:
\[ P = 8y - 8 \]

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