Some airlines have restrictions on the size of items of luggage that passengers

Question

Some airlines have restrictions on the size of items of luggage that passengers are allowed to take with them. Suppose that one has a rule that the sum of the length, width and height of any piece of luggage must be less than or equal to 222 cm. A passenger wants to take a box of the maximum allowable volume. If the length and width are to be equal, what should the dimensions be?
length = width = _______?
height = ________?
In this case, what is the volume?
volume = ________?
(for each, include units)

Please show work for this problem

Explanation / Answer

length = width = 74 cm height =74 cm In this case, what is the volume? volume = 405224 cm3

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