If a 100 by 104 rectangle is divided into unit squares, a diagonal line will pass through how many unit squares?

Question

3 by 3 square diagonal passes through 3 squares. 3 by 6 diagonal passes through 6 squares. The answer is not 104.

Answer 1

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!!!!