44 centimeters
The perimeter P of a rectangle is given as
P = 2(L + B) where L and B are the length and width respectively
Hence given that the perimeter is 172 centimeters and the width is 42 centimeters,
172 = 2(L + 42)
Divided both sides by 2
172/2 = 2(L + 42)/2
86 = L + 42
Subtract 42 from both sides
86 - 42 = L + 42 - 42
44 = L
The length of the rectangle is 44 centimeter