John painted his most famous​ work, in his​ country, in 1930 on composition board with perimeter 104.38 in. If the rectangular painting is 5.05 in. taller than it is​ wide, find the dimensions of the painting.

To find the dimensions of the painting, we can use the information provided:

1. **Perimeter of the rectangle**: 104.38 inches
2. **Relationship between height and width**: The height is 5.05 inches more than the width.

Let's denote the width of the painting by \( w \) inches. Then, the height of the painting would be \( h = w + 5.05 \) inches.

### Step 1: Express the perimeter formula for a rectangle.
The perimeter \( P \) of a rectangle is given by the formula:
\[
P = 2 \times (w + h)
\]
Substituting the given perimeter:
\[
104.38 = 2 \times (w + (w + 5.05))
\]

### Step 2: Simplify and solve for \( w \).
\[
104.38 = 2 \times (2w + 5.05)
\]
\[
104.38 = 4w + 10.10
\]
Subtract 10.10 from both sides:
\[
94.28 = 4w
\]
Divide both sides by 4:
\[
w = \frac{94.28}{4} = 23.57 \text{ inches}
\]

### Step 3: Find the height \( h \).
\[
h = w + 5.05 = 23.57 + 5.05 = 28.62 \text{ inches}
\]

### Final Answer:
The dimensions of the painting are:
- **Width**: 23.57 inches
- **Height**: 28.62 inches

Would you like any further details or explanations?

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Here are 5 related questions that expand on this problem:

1. What would the dimensions be if the height were 10 inches taller than the width?
2. How would the problem change if the painting were square?
3. What is the area of the painting?
4. How would you solve for the dimensions if the perimeter were given in centimeters?
5. How does the relationship between height and width affect the perimeter of a rectangle?

**Tip:** When solving geometry problems, drawing a diagram can help you visualize the relationships between different elements, like dimensions and perimeter.

Learn how to find the dimensions of a rectangle when given its perimeter and the relationship between height and width. This problem involves calculating dimensions using the perimeter formula and algebraic manipulation. Suitable for students in Grades 7-9.

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