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# help with math

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Pat has two sheets of large, square stamps. One sheet consists of  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 36 stamps arranged in a 6-by-6 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 18-by-18 sheet have?

Jan 30, 2021

### 2+0 Answers

#1
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The 3 x 3 sheet has 4 creases ...two vertical and two horizontal

each crease is  18/4 = 4.5 inches   and covers 3 stamps     so each stamp has a side length of 4.5/3 = 1.5 inches

The 6 x 6 sheet has  10 creases     5 vert   and 5 horiz

each crease covers 6 stamps

6    x 1.5   x 10 = 90 inches in a 6x6 sheet

Then you question asks about a 18 x 18 ....is that correct?

Jan 30, 2021
#2
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3  x  3    =  4 x 3 x 1.5  =  18

6 x  6    =    10 x 6 x  1.5  =   90

The formula  appears to  be  2 ( n-1) x n  x 1.5      where  we have an   n  x  n   arrangement

So

18 x 18   =  2(18-1)  x  18  x   1.5   =  34 x 18 x 1.5  = 918  inches   Jan 30, 2021