November's "Problem of the Month"

Trig and PreCalculus

Student's Name:  __________________________________________

Date Due:  Thursday November 30, 2017
Remember: You must submit your solution on THIS printed page.


Paper Cuts

Situation:
This month has two seperate questions, both related to cutting paper. If you choose, you can submit your answer by actually CUTTING paper to satisfy each puzzle. You should also support your cutting with a small written explanantion. (Note: For the first problem, be sure to give the requested final answer - the area of the original rectangle)

Paper Cuts Problem #1
A rectangular sheet of paper 2 inches by x inches (x > 2) is cut into three congruent pieces by two straight cuts, as shown.  Find the number of square inches in the area of the original rectangle. (not drawn to scale)

Paper Cuts Problem #2
Daniel folded a paper square twice. Then he made a single straight cut through all thicknesses.  When he unfolded the original square, he saw that he had cut out a square.
How might Daniel have folded and cut the paper?