What is a Double Rectangle?
A double rectangle is a rectangle that one side is 2x the other side.
What is a Special Rectangle?
A special rectangle is a rectangle that can be divided by 1, 2, 3, and 6, so it has to be a factor of 6. Why a number that can be divided by 6 is a special rectangle because it can be divided into smaller rectangles. For example, 6 is a special rectangle because it can be divided into twos.
What is a Double Special Rectangle?
This picture might not help you understand, but a double special rectangle follows the rules of both special rectangles and double rectangles. Look up at the article “What is a Double Rectangle?”, then look at the article below. Try figuring out a double special rectangle. If you need help, look at the article below this one.
How can you find all of the Double Special Rectangles?
Start with a special rectangle. Then, divide by 2, then see if that’s a square number. For example, 18. Divide that by 2, and you’ll get 9. If you know that 18 is a special rectangle, then you don’t need to read this. 18 is a special rectangle because it can be divided by 1, 2, 3, and 6. That is one way to find all of the double special rectangles. However, the 2nd way to do this is this. Look at the picture below. Then type in the comments if you learned something new.
Special Rectangle Area Divided by 2 Is that a square number?
6 3
12 6
18 9 YES
24 12
30 15
36 18
42 21
48 24
54 27
60 30
66 33
72 36 YES
78 39
84 42
90 45
96 48
102 51
108 54
114 57
120 60
126 63
132 66
138 69
144 72
150 75
156 78
162 81 YES
168 84In the second column you see they are 9, 36, and 81. The pattern is every 3 square numbers can find you all of the double special rectangles.
