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!
To find the maximum possible length of the luggage, we need to find the perimeter of the base and subtract it from the given sum.
The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the width is given as 15 inches and the length is what we need to find.
Let's denote the length of the luggage as L. The sum we are given is the height of the luggage (20 inches) plus the perimeter of the base, which is 2 times the width plus 2 times the length. So we can write the equation as:
20 + 2(15) + 2L <= 110
Simplifying this equation, we get:
20 + 30 + 2L <= 110
50 + 2L <= 110
2L <= 110 - 50
2L <= 60
Dividing both sides by 2, we find:
L <= 30
Therefore, the maximum possible length of the luggage is 30 inches. So yes, the correct answer is 30 inches.