https://file.aiquickdraw.com/mathbot/file/1730020498490nr28ytfb.jpg

To solve this problem, let's break down the information given.

### Problem Statement
1. **Initial Information**:
   - Let the breadth of the rectangle be \( b \).
   - The length \( l \) of the rectangle is 2 more than 3 times the breadth. Therefore, \( l = 3b + 2 \).

2. **Original Perimeter**:
   - The perimeter \( P \) of a rectangle is given by \( P = 2(l + b) \).
   - Substituting for \( l \): \( P = 2((3b + 2) + b) = 2(4b + 2) = 8b + 4 \).

3. **Modified Condition**:
   - Both the length and breadth are increased by 3 units. So, the new length \( l' = (3b + 2) + 3 = 3b + 5 \) and the new breadth \( b' = b + 3 \).
   - The new perimeter \( P' = 2(l' + b') = 2((3b + 5) + (b + 3)) = 2(4b + 8) = 8b + 16 \).

4. **Condition on Perimeters**:
   - The new perimeter is twice the original perimeter. So, \( P' = 2P \).
   - Substituting for \( P' \) and \( P \): 
     \[
     8b + 16 = 2(8b + 4)
     \]
     Simplify this equation:
     \[
     8b + 16 = 16b + 8
     \]
     \[
     16 - 8 = 16b - 8b
     \]
     \[
     b =

The length of a rectangle is 2 more than 3 times its breadth. If both length and breadth are increased by 3 units, the new perimeter becomes 2 times the original. Find the length and breadth of the rectangle.

Learn to solve a rectangle geometry problem where the length is 2 more than 3 times its breadth. Explore how the perimeter changes when dimensions are increased, with a detailed algebraic solution suitable for Grades 7-9.

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