March 2013
Problem of the Month

Rectangle Problem

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

Send any comments or questions to: David Pleacher