How is this possible?

for the first one, the slope of the hypotenuse is 5/13

for the second one, the hypotenuse is not a straight segment. Its made up two smaller segments. One has slope of 2/5 and the other one has slope of 3/8

look closely at the purple triangles and blue triangles. There is a slightly difference. Use the squares as the guide

The slope of the purple triangle is 3/8 while that of the blue one is 2/5. These are not equal, so the big triangly thing in both pictures is actually not a triangle - it changes slope part way through!! The change of slope occurs at different points, so the big triangly things are actually different and differ in area by one.

by rearranging the placement you left a gap. but they are not all the same shape, there is on that has a minor difference. the green boxes. the one on the top left has part of the corner cut off. just something i noticed.

this is a proof that you can rearrange things and get different answers.

well that is my thoughts on it. good luck

because they have the same area with the same area you could hacve the same boxdes and maybe because they are have of a square and when the both of them are put together they make one square so that means that they have the same amount of squares and sizes of squares