Let w represent the width of the rectangular painting.
If the rectangular painting is 5.14 in. taller than it is wide, it means that
length = w + 5.14
The formula for calculating the perimeter of a rectangular is
Perimeter = 2(length + width)
Given that perimeter = 107.69, then
107.69 = 2(w + 5.14 + w)
107.69 = 2(2w + 5.14)
107.69 = 4w + 10.28
4w = 107.69 - 10.28 = 97.41
w = 97.41/4
w = 24.35
length = 24.35 + 5.14
length = 29.49
The dimesions are
width = 24.35 in
height = 29.49 in