When the large rectangle in this picture is cut in the manner shown,
the pieces can be rearranged to form a square.
What is the perimeter of the square?
Solution to the Problem:
The perimeter is 48 units.Since it is a rectangle, you can use the Pythagorean Theorem to
obtain the missing sides along the perimeter.
There are two 3-4-5 triangles and one 9-12-15 triangle.
Therefore, the large rectangle has dimensions 9 x 16.
Its area is equal to 144 square units, which must be the area of the square.
So each side of the square must be 12 units long and its perimeter = 4 x 12 = 48 units.
The figures below show the missing sides, and how to form the square.
Correctly solved by:
| 1. James Alarie | Flint, Michigan |
| 2. Riley Dolezal |
Mountain View High School, Mountain View, Wyoming |
| 3. Trystin Walker |
Mountain View High School, Mountain View, Wyoming |
| 4. Blace Martin |
Mountain View High School, Mountain View, Wyoming |
| 5. Dylan Martin |
Mountain View High School, Mountain View, Wyoming |
| 6. Marshal Liebman | Aiken, South Carolina |
| 7. Chad Fore | Gate City, Virginia |
| 8. Ryan Woody |
Mountain View High School, Mountain View, Wyoming |