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?
+40 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)
+129850 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) =
12
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 =
270 inches
