Ira S. answered • 10/06/15

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Well, this is an interesting question. Trying to find a pattern is the right way to go. I first reduced your rectangle to a rectangle that has dimensions of 25 by 26, since the diagonal of the full rectangle will also pass through the corner of this rectangle....this will happen 4 times for your full diagonal. It's kind of like slope....you did a 3 by 6 rectangle already. a slope of 3/6 is the same as the slope 1/2.....3 times, if you know what I mean.

I then drew rectangles with dimensions which have no common factors. like a rectangle of 2 by 3 or 3 by 7. This is what I found.

dimensions number of squares diagonal passes through

2 by 3 4

2 by 5 6

3 by 4 6

4 by 7 10

5 by 9 13

3 by 7 9

I'm pretty convinced that you add the 2 dimensions and then subtract 1when the dimensions are reduced like I did.

So, I think your answer should be 25 + 26 - 1 which is 50. then multiply that by 4 to get 200.

Hope this helped.....and I think it's correct!!!!

Crystal S.

Draw a 9 by 3 rectangle on a square grid. Draw one diagonal. How many squares does the diagonal pass through?

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Angelica D.

10/06/15