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.)

To find the dimensions of the painting, we can set up the equations based on the information given. Let the width be \( x \) inches. Since the painting is 5.65 inches taller than it is wide, the length would be \( x + 5.65 \) inches. The perimeter of a rectangle is given by the formula \( P = 2(\text{width} + \text{length}) \). We know the perimeter is 103.59 inches, so we can write: \[ 2(x + (x + 5.65)) = 103.59 \] Simplifying, we get: \[ 2(2x + 5.65) = 103.59 \\ 4x + 11.30 = 103.59 \\ 4x = 103.59 - 11.30 \\ 4x = 92.29 \\ x = \frac{92.29}{4} \\ x = 23.07 \text{ inches (width)} \] Now, for the length: \[ \text{Length} = x + 5.65 = 23.07 + 5.65 = 28.72 \text{ inches} \] So the dimensions of the painting are: Width: **23.07 inches** Length: **28.72 inches**