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We are given two rectangles, P and Q, with the following information:

- Rectangle P has a perimeter of 20 inches.
  - One side is \( h \), and the other is \( j + 4 \).
  
- Rectangle Q has a perimeter of 30 inches.
  - One side is \( 3h \), and the other is \( j + 1 \).

### Perimeter Formulas:
The perimeter \( P \) of a rectangle is given by:
\[
P = 2 \times (\text{length} + \text{width})
\]

### Setting up the equations:
1. **Rectangle P's Perimeter**: 
   \[
   20 = 2 \times (h + (j + 4))
   \]
   Simplifying:
   \[
   20 = 2 \times (h + j + 4) \quad \Rightarrow \quad 20 = 2h + 2j + 8 \quad \Rightarrow \quad 12 = 2h + 2j \quad \Rightarrow \quad 6 = h + j
   \]
   This gives us the first equation: 
   \[
   h + j = 6 \quad \text{(Equation 1)}
   \]

2. **Rectangle Q's Perimeter**: 
   \[
   30 = 2 \times (3h + (j + 1))
   \]
   Simplifying:
   \[
   30 = 2 \times (3h + j + 1) \quad \Rightarrow \quad 30 = 6h + 2j + 2 \quad \Rightarrow \quad 28 = 6h + 2j
   \]
   This gives us the second equation:
   \[
   6h + 2j = 28 \quad \text{(Equation 2)}
   \]

### Solving the system of equations:

We now have the system of two equations:
1. \( h + j = 6 \)
2. \( 6h + 2j = 28 \)

From Equation 1, solve for \( j \):
\[
j = 6 - h
\]

Substitute this into Equation 2:
\[
6h + 2(6 - h) = 28 \quad \Rightarrow \quad 6h + 12 - 2h = 28 \quad \Rightarrow \quad 4h + 12 = 28 \quad \Rightarrow \quad 4h = 16 \quad \Rightarrow \quad h = 4
\]

Now substitute \( h = 4 \) back into Equation 1:
\[
4 + j = 6 \quad \Rightarrow \quad j = 2
\]

### Final Answer:
The values of \( j \) and \( h \) are:
\[
j = 2, \quad h = 4
\]

Would you like further details or have any questions?

Here are 5 follow-up questions for deeper understanding:
1. How would the solution change if the perimeter of rectangle P was different?
2. What if rectangle Q had sides proportional to a different constant than \( 3h \)?
3. Can you solve for the area of each rectangle using the values of \( j \) and \( h \)?
4. What other shapes besides rectangles have similar perimeter formulas?
5. How would you solve for perimeter if one of the dimensions was a variable expression?

**Tip**: When solving for variables in two equations, always simplify and substitute systematically to avoid errors.

Two rectangles are shown below. Rectangle P has a perimeter of 20 inches. Rectangle Q has a perimeter of 30 inches. Rectangle P has sides h and j + 4, and Rectangle Q has sides 3h and j + 1. What are the values of j and h?

Solve a geometry problem involving two rectangles with given perimeters. Use algebra and the perimeter formula to find the dimensions of the rectangles, applying a system of linear equations. Suitable for students in Grades 6-8.

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