Right

 

Well ive screen shotted them and they do fit exactly over one another, and we prosume the writing along with the triangles is true.

 

So im stuck, but im sure theres a really simple explanation which you can all see and im jus being dumb. The only thing i have noted is that when placed over the top of each other the lower triangle's hypotonuse does seem to bulge slightly.

I've seen this question before unfortunately, so I might spoil the fun. I'll kind of try put it in spoiler tags. Highlight below to read:

 

This problem exploits our inability to discern the difference of the area along the hypotenuse. If you look closely enough to the area along the hypotenuse, you will see that there is indeed a difference. The top figure shows more coverage.

 

Mathematically, you can see that the triangles are NOT congruent. This is the main cause of the discrepency. They deviate by so little that it is hard to see visually.

 

The composed "triangle" has a tan of 5/13 blocks (0.3846), the red with 3/8 (0.375), and the green with 2/5 (0.4). The overall shape is in fact not a triangle but a 4 sided polygon. There is a small angle between where the red and green triangles just touch

We need to count the square occupied as the above shape is not a triangle.

That's what I think.

No worring about "fun" i think i see it. Although the triangles still seem to fit over each other. Maybe thats what the "bulge" was that i was talking about.

These are not right triangles because the hypotenuse in the upper triangle is bent slightly up, while the hypotenuse in the lower one is bent slightly down.

 

If you calculate the tangent in the first sub triangle and then carry that same angle to the whole triangle, then the opposite side should be 4.875 units long instead of 5 units.

hasn't there already been a thread on this? you can look at it and see that the top one isn't even a triangle.

hasn't there already been a thread on this? you can look at it and see that the top one isn't even a triangle.

Neither is the bottom one (even filling in the open square) !

 

Simply put [imath]2/5 \neq 3/8[/imath]