math
posted by Julia Ten .
in order for piece of rectangular luggage to fit in the overhead compartment of a certain airplane, the sum of the height of the luggage and the perimeter of the base of the luggage must be less than or equal to 110 inches. If a piece of luggage has a height of 20 inches and a width of 15 inches, what is the maximum possible length of the luggage?
is the correct answer 30?

Yes.
They are saying :
height + base 1 + base 2 + base 3 + base 4 has to be equal to or less than 110 inches.
You're right because there are 4 lines in the perimeter of the base. If you draw a square or rectangle, it has four lines.
2 of those lines are 15 inches. 15x2 = 30.
The height is 20.
30+20 = 50
So you have 60 inches to play with. They did not tell you the length of the luggage, but on that square, the length takes up 2 sides of the square. So 60 inches left over divided by the 2 sides of the rectangle left over = 30 inches per side.
Nice work!