Question

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 18cm.

On the second piece of paper, Pat draws straight lines that divide the paper into a 6-by-6 grid of squares.
what is the total length of the lines that Pat draws on the second piece of paper?

Answer 1

45!!

Explanation:

Answer 2

45 cm

Explanation:

2 lines will divide the square in thirds. 2 additional lines will divide those thirds into ninths. Pat's 4 lines total 18 cm.

To divide the square into sixths requires 5 lines. To divide it into 36ths requires 5 additional lines. Hence the total number of lines on the second paper is 10/4 = 5/2 times the total on the first paper.

The total length of lines on the second paper is ...

(5/2)(18 cm) = 45 cm