Perimeter of a rectangle = 2L + 2W = 146
"width is 10 longer than twice the length"
translates to
W = 2L + 10
this can be rearranged to be
2L = W - 10
we can plug that into the first equation and get
(W - 10) + 2W = 146
add like terms
3W - 10 = 146
add 10 to both sides
3W = 156
divide both sides by 3
W = 52
therefore the width is 52 cm