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Pat starts with two identical square pieces of paper. On the first one, she draws straight lines that divide the paper into a 3-by-3 grid of squares. The total length of the lines she draws is 18. On the second piece of paper, Pat draws straight lines that divide the paper into a 16-by-16 grid of squares. What is the total length of the lines that Pat draws on the second piece of paper?

 Mar 8, 2022
 #1
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What is the total length of the lines that Pat draws on the second piece of paper?

 

Hello Guest!

 

\(l=\dfrac{18}{2(3-1)}\cdot 2(16-1)=\color{blue}135\)

 The total length of the lines that Pat draws on the second piece of paper is 135.

laugh  !

 Mar 8, 2022
 #2
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Pat starts with two identical square pieces of paper. On the first one, she draws straight lines that divide the paper into a 3-by-3 grid of squares. The total length of the lines she draws is 18. On the second piece of paper, Pat draws straight lines that divide the paper into a 16-by-16 grid of squares. What is the total length of the lines that Pat draws on the second piece of paper?    

 

To divide the first paper into 3x3 grids, she has to draw 4 lines, 2 vertical and 2 horizontal.  

 

Since the total length of these lines is 18, then one line is 18/4 = 4.5.  

 

To divide the second paper into 16x16 grids, she has to draw 30 lines, 15 vertical and 15 horizontal.  

 

Since each line is 4.5, then the total length is (30)(4.5) = 135.   

.

 Mar 8, 2022

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