Pat has two sheets of large, square stamps. One sheet consists of 9 stamps arranged in a 3-by-3 square. (That's 3 stamps by 3 stamps, not 3 inches by 3 inches.) The other sheet consists of 100 stamps arranged in a 10-by-10 square. The stamps on each sheet are separated by perforated creases. All the stamps on both sheets are the same shape and size.
The total length of the creases on the 3-by-3 sheet is 18 inches.
How many inches of creases does the 10-by-10 sheet have?
If the 3x3 and 10x10 square have the same proportions meaning they have same sized stamps and same sized creases, it's just a proportionality problem so take the area of the 10x10 over the 3x3 100/19. The multiply that by the length of the creases on the 3x3 sheet to get 200.
(Correct me if I'm wrong)
This is similar to the toothpick problem
Number of perforations in the 3 x 3 sheet
Number of stamps in each row * ( 3-1) rows + Number of stamps in each column * ( 3 - 1) columns =
(3) (3-1) + (3) ( 3-1) =
3(2) + 3 (2) =
So each perforation = 18 inches / 12 = 1.5 in
Using the same reasoning applied to the 10 x 10 sheet
(10 (10 - 1) + 10 (10 - 1) =
10 (9) + 10 (9) =
90 + 90 = 180 perforations
180 * 1.5 =