Rectangle is not a square. Rectangle is a square. Use the possible segment lengths to find the missing segment length.

1. If segment is 5 units long and segment is 2 units long, how long would segment  be?

2. If segment is 10 units long and segment is 6 units long, how long would segment  be?

3. If segment is 12 units long and segment is 5 units long, how long would segment  be?

4. If segment is 9 units long and segment is 5 units long, how long would segment  be?

Rectangle has been decomposed into squares.

Tiling of rectangle KXWJ with 2 large squares, KJST and TSUV; 3 medium squares, GUWH, KGHL, and MILN; 1 small square, VMOP; and 2 tiny squares, QONR and PQRX. TSUV and KJST are stacked horizontally. TSUV is on the right of KJST. GUWH, KGHL, and MILN are stack vertically. All 3 are on the right of TSUV. VMOP is below MILN. QONR and PQRX are stacked vertically. Both are on the right of VMOP.  

Segment is 33 units long and segment is 75 units long. Find the areas of all of the squares in the diagram.

Rectangle is 16 units by 5 units.

1. In the diagram, draw a line segment that decomposes into two regions: a square that is the largest possible and a new rectangle.

2. Draw another line segment that decomposes the new rectangle into two regions: a square that is the largest possible and another new rectangle.

3. Keep going until rectangle is entirely decomposed into squares.

4. List the side lengths of all the squares in your diagram.

Draw a rectangle that is 21 units by 6 units.

1. In your rectangle, draw a line segment that decomposes the rectangle into a new rectangle and a square that is as large as possible. Continue until the diagram shows that your original rectangle has been entirely decomposed into squares.

2. How many squares of each size are in your diagram?

3. What is the side length of the smallest square?

Draw a rectangle that is 28 units by 12 units.

1. In your rectangle, draw a line segment that decomposes the rectangle into a new rectangle and a square that is as large as possible. Continue until the diagram shows that your original rectangle has been decomposed into squares.

2. How many squares of each size are in your diagram?

3. What is the side length of the smallest square?

Write each of these fractions as a mixed number with the smallest possible numerator and denominator:

What do the fraction problems have to do with the earlier rectangle decomposition problems?