NOTE: This is the last problem of the semester. The Problem of the Week will resume at the start of the Fall Semester in early September. Enjoy your summer break.

Ignoring the weight, a package will be accepted for shipping by the United Parcel Service if its length plus girth is no larger than 130 inches.  See figure on the left.  (The length is the longest dimension while the girth is twice the sum of the other two dimensions.)

What is the size of the square window of smallest area through which you can pass all acceptable packages?

For a heartier meal:  What is the size of the rectangular window of smallest area though which you can pass all acceptable packages?