If the width is w then length is 2w+6 (cm). The area is w(2w+6)=480.
That is, 2w²+6w-480=0, w²+3w-240=0.
Using the formula, w=(-3±√(9+960))/2=(-3±√969)/2=(-3±31.1288)/2.
We need the positive square root, so w=14.0644cm approx. The length is 2w+6=34.1288cm.
It’s unusual for questions of this type to have an irrational solution, so there may be an error in the question.
For example, if length=2w+16 instead of 2w+6, then the area is w(2w+16)=480.
That is, 2w²+16w-480=0, w²+8w-240=0=(w+20)(w-12). The width is therefore 12cm and the length=2w+16=40cm.