the perimeter of some traffic sign must be 150 inches also its length is 15 inches longer than its width, find the dimensions of this sign

Answer 1

You don't say what shape your traffic sign is.
e.g.
a stop sign is a regular octogaon, yours can't be that
a yield sign is an equilateral triangle, not yours
etc.

Answer 2

however, since you mention only length and width, let's assume a rectangle.

2(w+(w+15)) = 150
4w + 30 = 150
w = 30

the sign is 30x45