If the length of a rectangle is doubled and its breadth is tripled, what is the new perimeter?

Answer

To find the new perimeter of a rectangle when its length is doubled and its breadth is tripled, we can follow these steps:

### Step 1: Understand the formula for the perimeter of a rectangle.
The formula for the perimeter (P) of a rectangle is given by:
\[ P = 2 \times (L + B) \]
where \( L \) is the length and \( B \) is the breadth.

### Step 2: Define the original dimensions.
Let:
- \( L \) = original length of the rectangle
- \( B \) = original breadth of the rectangle

### Step 3: Determine the new dimensions.
According to the problem:
- The new length (L') is double the original length:
\[ L' = 2L \]
- The new breadth (B') is triple the original breadth:
\[ B' = 3B \]

### Step 4: Substitute the new dimensions into the perimeter formula.
Now, we can find the new perimeter (P'):
\[ P' = 2 \times (L' + B') \]
Substituting the new dimensions:
\[ P' = 2 \times (2L + 3B) \]

### Step 5: Simplify the expression.
Now, simplify the expression:
\[ P' = 2 \times (2L + 3B) = 4L + 6B \]

### Final Answer:
Thus, the new perimeter of the rectangle is:
\[ P' = 4L + 6B \]

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