Can you solve it?

[Juice Box]

Triangle Problem

My friend have stupid explinations for it, but i simply do not believe them, it seems impossible, but i guess its not, unless you know howTriangle Problem

 

[Juice Box]

Sorry bout broken link there, clicked https now it works

 

[imported_lev]

the top line on the bottom figure is not straight. in fact if you drew a straight line from each of the end points you would get a trianle with the same area of the square divided by two. This is a little hard to see since the borders of each shape are comparatively thick.

Notice that the top figure is not a trangle. And if you drew a line connecting each of the end points of the top line of the top figure, you would get a trianle. And the area of the triangle is the other half of the area for the square.

 

[ss284]

Take a look at the dimensions (base x height) of the "triangle" (5 x 13). Then take a look at the dimensions of the two triangles used to make the hypotenuse of the triangle. Realize that they do not match the dimensions of the original triangle (2 x 5) and (3 x 8). They are close, tricking your mind into thinking that the angle of the hypotenuse in respect to the base is the same, when they are in fact not. Both of the figures (ignoring the little gap in the second) you are looking at aren't triangles, they are infact 4 sided shapes(there is an edge where both triangles touch). That gives you the illusion they are the same shape, when they arent. Add up the area of each of the separate objects using basic math. You have the same area. This is just the illusion of a triangle, when it actually isnt, thus 1/2(b*h) cant be used to accurately calculate the area.

-Steve

 

[Juice Box]

oh wow, i didnt even see that! Now i understand, except why is the top figure not technically a triangle? because the bottom line isint really straight?

 

[ss284]

Originally posted by: digitalsnare
oh wow, i didnt even see that! Now i understand, except why is the top figure not technically a triangle? because the bottom line isint really straight?

Because the hypotenuse isnt straight.

 

[Juice Box]

is it concave towards the right angle, it lookes curved

 

[ss284]

Im too lazy to think any more, but I would think the first triangle without the extra gap has a concave hypotenuse, while the second triangle has a convex hypotenuse. I could be wrong since im hungry.


Lunch time, cya.

-Steve

 

[PacFu]

no no no, its has nothing to do with angles...

the question here is area and volume, not angles.

Ok, forget the fact there are the red and green triangle, lets just concentrate on the middle 2 shapes and the rectangle it forms. Simple Tetris math here

Area = L x W

On the top triangle (lets call it TriA) the area of the rectangle is 5x3=15
The bottom, TriB, the rectangle area is 8x2=16

There is where the hole comes from.

Why? As a whole you are dealing with volume, not area. I'm too tired to figure hypotenuses.

 

[ss284]

Originally posted by: PacFu
no no no, its has nothing to do with angles...

the question here is area and volume, not angles.

Ok, forget the fact there are the red and green triangle, lets just concentrate on the middle 2 shapes and the rectangle it forms. Simple Tetris math here

Area = L x W

On the top triangle (lets call it TriA) the area of the rectangle is 5x3=15
The bottom, TriB, the rectangle area is 8x2=16

There is where the hole comes from.

Why? As a whole you are dealing with volume, not area. I'm too tired to figure hypotenuses.

Maybe you should look a little closely, as you dont seem to understand the significance of the puzzle. It actually has everything to do with angles, especially when dealing with triangles. If the triangles arent similar to each other as well as the larger triangle, then the whole shape isnt a triangle.


-Steve

 

[ss284]

Originally posted by: PacFu
no no no, its has nothing to do with angles...

the question here is area and volume, not angles.

Ok, forget the fact there are the red and green triangle, lets just concentrate on the middle 2 shapes and the rectangle it forms. Simple Tetris math here

Area = L x W

On the top triangle (lets call it TriA) the area of the rectangle is 5x3=15
The bottom, TriB, the rectangle area is 8x2=16

There is where the hole comes from.

Why? As a whole you are dealing with volume, not area. I'm too tired to figure hypotenuses.

BTW, volume is a measurement of 3 dimensions. Area is a measure of 2 dimensions. Unless I'm blind, I dont see that extra 3rd dimension, since triangles are 2 dimensional objects, as are all the shapes in this problem.

-Steve

 

[silverpig]

Hold a piece of paper along the hypotenuses (sp?) of the two large triangles to see why.

 

[imported_lev]

I believe that's "hypoteneese"

 

[Peter]

... and here's another one of the "problems" that recur every month or so.

Without looking: 2/5 does not equal 3/8. The big shape is not a triangle.

 

[wacki]

Originally posted by: Peter
... and here's another one of the "problems" that recur every month or so.

Without looking: 2/5 does not equal 3/8. The big shape is not a triangle.

Yup. Noobs, gotta love em.

 

[Juice Box]

are you calling me a noob?

 

[jay75]

the top triangle has a concave hypotenuse(pushed inwards), and the bottom triangle has a convex hypotenuse(pushed outwards). the top vertex of the green triangle in the bottom picture, is well above the point it should be in, had that same triangle been put in the top picture. and the left most vertex of the green triangle in the top picture, does not correspond with where the line cuts in the bottom picture. the convex triangle(if you can call it that now!) minus the area of the concave triangle is equal to the "hole" in the second triangle. but it's a nice trick anyhow!

 

[Peter]

If it's not straight it's not a hypotenuse. But you're correct in that the loooong razor thin difference between the inward and outward bent ramps is exactly one square.

 

[Geniere]

I first saw this "puzzle" at least 10 years ago. It's as crooked now as it was then.

 

[Cogman]

yep, this is a Repost, and yes IMO it is pretty easy to see that there is a bump in the hypotenuse

 

[Mday]

yeah, i couldnt get it the first time i saw it many years ago... its still not a triangle =D