Brainteaser

One problem lies in the fact that the orange triangle and the teal triangle aren't perfectly similar.

slope = y/x

teal's slope = 2/5
orange's slope = 3/8

someone check my math on this, cuz this seems even curiouser:

area of top triangle = .5 x 5 x 13 = 32.5

area of red = .5 x 3 x 8 = 12
area of teal = .5 x 2 x 5 = 5
area of yellow = 7
area of sage = 8
(like my fancy color names?)

sum of areas of shapes = 32

so the difference in areas is .5 units!?!?!?

but there is a missing block of area = 1 ??

i am also confused

and i don't understand where yr going with that paul, my maths are rusty!

oh yes! you are right... so the long (not-really-a) hypotenuse is not actually a straight line. therefore the original shape is not a triangle at all.

Is "similar" what I mean? Maybe not.

But the whole triangle has a slope of 5/13.

2/5 = 0.4
5/13 = 0.385
3/8 = 0.375

In a proper situation these slopes should all be the same.

I guess what this means is that the so-called hypotenuses of the big triangles aren't even straight lines! (Yes, Ron, I see your post now. Hi-five!)

I don't have a straight-edge, and if I did I'd feel silly holding up to my screen. But I think the first shape is bent a little inward and the second shape is bent a little outward, where the teal and the orange triangle meet. This allows the second one to have a little more area -- one square's worth.

gold star for paul!

all I can see is a red cross!!!

Yeah, I think that must be it. Thanks - but it's still so bizarre to look at!

Oh and what the heck - since the thread's here already, does anyone have any more of these?

yes, well done Paul and ron. The two "triangles" are not in fact identical. haha I haf been staring at the pic too closely, the whole thread now seems to have "wallpaper" with squares like in the pic!