Chapter 4.6, Problem 47MS

Here we celebrate the power of algebra as a powerful way of finding unknown quantities by naming them, of expressing infinitely many relationships and connections clearly and succinctly, and of uncovering pattern and structure.

Measuring moment (H). While lounging around your room one day, avoiding your history reading, you notice a tissue box and decide to do some measuring. The box has dimensions l, w, and h, measured in inches. Your measurements reveal that the perimeters of the faces have the following lengths: $\text{2l + 2w = 26,21 + 2h = 24, and 2w + 2h = 14}\text{.}$

While it might not help you with your history assignment, solve these equations simultaneously to find l, w, and h.