College Algebra
posted by BFG .
Sandy is going on a business trip to Washington state. She has a 46 inch umbrella to pack since she will be there during rainy season. She plans to pack the umbrella in the diagonal of her suitcase, but she has to buy the suitcase first. The airline company will allow a suitcase to be 24 inches long. When Sandy buys the suitcase, how wide to the nearest tenth does the suitcase need to be for the umbrella to fit?

Assuming she buys a 24" suitcase, then
24^2+w^2 = 46^2
w = 39.24
odd; width is usually less than length
Now, if you add a 3rd dimension, so the umbrella can lie between opposite corners of the 3D space, then you have, for height h,
24^2 + w^2 + h^2 = 46^2