Using Geometry to Solve Design Problems Practice Test

A shipping company uses a rectangular box with interior dimensions $30\text{ in} \times 20\text{ in} \times 18\text{ in}$. A rigid rectangular sign must fit flat on the bottom (so it must fit within the $30\text{ in} \times 20\text{ in}$ base). The sign cannot be bent, and its side lengths are whole numbers of inches.

Which design choice is valid?

A garden path is a rectangle $12\text{ ft}$ long and $8\text{ ft}$ wide. A rectangular flower bed must be placed inside it so that there is a uniform border of $1\text{ ft}$ of path on all sides. The flower bed’s side lengths must be whole numbers of feet.

Which design satisfies all constraints?