John painted his most famous work, in his country, in 1930 on composition board with perimeter 103.59 in. If the
rectangular painting is 5.65 in. taller than it is wide, find the dimensions of the painting.
What is the width? 23.07 in.
(Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.)
What is the length?
(Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.)

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UpStudy AI · Accepted Answer

To find the **length** of John’s painting, we can use the information provided:

1. **Perimeter of the rectangle:** $$ P = 103.59 $$ inches
2. **Width (w):** $$ 23.07 $$ inches
3. **Length (l) is 5.65 inches taller than the width:** $$ l = w + 5.65 $$

First, let's verify the relationship using the formula for the perimeter of a rectangle:

$$
P = 2(w + l)
$$

Substitute the known values:

$$
103.59 = 2(23.07 + l)
$$

$$
51.795 = 23.07 + l
$$

$$
l = 51.795 - 23.07
$$

$$
l = 28.725 \text{ inches}
$$

Rounded to two decimal places:

$$
l = 28.72 \text{ inches}
$$

**Answer:**  
**28.72 in.**
The length of the painting is 28.72 inches.

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