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- Thread starter ValVed RaY
- Start date

K

that's true but this question mathematically is ment to for u to solve it according to the "large triangle" the angle changed there fore the area changed

K

the area of the smaller shapes never changed

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Yeah so easy to figure out after you read the solution posted by someone else.Originally posted by Pressure

The area will always be the same because the shapes never change size... and the parts a rearranged so thats why you get that extra square.

A first grader could figure that out jeez.

p.s. you don't sound very smart

/me gives out prize to pressure

:cheers:

:cheers:

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Originally posted by Chris_D

How is it solved?

I drew the shapes out to scale and set them up and coloured them like the top picture.

I make a copy of the top picture and rearrange it like the bottom. No fancy convex, concave...

and....

You dont know that the empty space is an exact grid space, which I can tell it isnt. Its a rectangle, sombody measure it. The hypos are different to make it exact I believe.

EDIT: well, maybe not, the hypos may be doing something else.

BTW guys I always make alot of edits so bear with me.

K

none of u used trigs

K

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I've done it all on the grid with totally straight triangles and it doesn't make a difference from the pic in the first post.

C

Each of the shapes in the first picture are the same size as the corresponding shapes in the second picture. The hypotenuse is bent in both pictures. It is not bent because of a flaw in the drawing, it is bent because the slopes of the two triangles are different. The slope of the green triangle is 2/5 units, while the red triangle is 3/8 units. 3/8 cannot be reduced to 2/5, so the hypotenuse would be bent, both in a computer representation and when calculated. The size of each shape does not change and as such the summation of the areas does not change.

Area of green triangle - 5

Area of red triangle - 12

Area of light green figure - 8

Area of yellow figure - 7

The total area of all the shapes added together is 32 for both figures. Now, let's pretend for a moment that the hypotenuse in the first triangle is straight, both geometrically and in the computer representation. That would make its area 1/2*13*5=32.5. That is one half of a unit more than what we know the actual area is. Since we know that the hypotenuse on the first figure is concave, it is easy to see where the half a unit comes from (the empty space in the bend.)

So, we now have half a unit accounted for in the bottom triangle, where does the other half come from? By swapping the triangles you now have a convex bend, which simply comes out to be another half a unit hanging out of a 13 by 5 triangle. Those two half units come together in the mysterious white space.

Simple geometry and spacial reasoning, really ^_^.

G

Originally posted by Gojin

Rod is saying, draw it out on a program where you can snap to grid, then draw the same shapes. See if it still happens.

I did. It's called AutoCAD...you may have heard of it. If I had brought my HP 48G home from work, I could have done it quicker than drawing it out. Look, I deal with angles every day for a living. I get paid to be as correct as possible. Those angles I gave in my first post are accurate to the decimal degree I put them in.

My last post on this. //waits for applause//

Both triangles (by that I mean the red triangle and the dark green triangle) are made with straight lines, just different angles. In the first arrangement, the different angles create an obtuse angle that is "open" upward. If you drew a

I give up.

[edited for some wording that may be confusing]

K

lol use the trig definitions and it would be impossible for the two figures to share the same area

B

Originally posted by Reaper978

This is definately not an easy problem.

Thank you Captain Obvious! :-p

Good lord, where do you people find this stuff?

Slope = y2 - y1 / x2 - x1 or just y/x

So...

Red Triangle slope is 3/8 = .375

Blue Triangle slope is 2/5 = .4

Therefore lining them up in the picture is incorrect, the overall shape of the object is not a triangle. Both slopes would have to be the same

I think it has to do with WHERE the slope change is... When the slope is changed at the top, it leaves more area under it, as opposed to the other way around. I don't know what the answer is, but I know the Hypt. answer is wrong. I'm too tired to think.. nite nite

Edit: Yes, CyberGeek is correct.. That's what I was hinting at. He is right. He posted while I was typing. gj CyberGeek!

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everything is snapped to the grids

i zoomed in, showing that the shapes could not possibly fit in the arrangement

K

so any chance u guys are passing the time for the vid?

S

X

Originally posted by Slash

CyberGeek wins.

The Hypotenuse answer is wrong.

well the right answer was also on the first page of thise thread......twice....

S

Just read throught this whole thread. Looks like a some people have already answered it correctly

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If you were to compare the constructed shaped of two such objects (like if you tried cutting these out for example) you would find that the total object is not a triangle. It is a 4 sided object with a nearly 180 degree angle on one side (ALMOST a straight line). This is the "concave/convex" difference that people have been pointing out.

Now, many have said "ignore that - it was just drawn wrong". No, it wasn't. The fact of the matter is that you CAN NOT draw this object with a straight 'hypotenuse' without changing the shape of the constituent objects from one construct to the next. In other words, the only way these fit together like that is if your "triangle" has a bent edge. Bent inward in one case and bent outward in the other. Without the bend, you'd find odd gaps in the construction and it would be OBVIOUS where the hole comes from. Try it - print the first diagram out on some paper. Cut the top "triangle" out using your very best scissors skills (remember not to run with scissors and don't poke your eye out) and be sure to stay on the lines. For fun, try making a version with the "corrected" unbent "hypotenuse". You'll notice that your "triangle" won't quite fit together in the other configuration.

M

The hypotenuses are different, the top one is concave, the bottom one is convex. They change angles when they touch the corner or the yellow/orange peice

Originally posted by Folder

The red triangle is three squares high, the teal triangle is two squares high. When switched, it forces the other orange and green squares to a smaller space, thus making a 'gap' since they were not intended to fit in a different pattern... Simple geometry.

Like loads of you have said, Folder was right.

G

Originally posted by Folder

The red triangle is three squares high, the teal triangle is two squares high. When switched, it forces the other orange and green squares to a smaller space, thus making a 'gap' since they were not intended to fit in a different pattern... Simple geometry.

Folder and spitzfiya you are patethic!!! Pretending you see the solution "it's so obvious" believing oyua re some **** geniuses, and your explanation does not even make ANY sense.

Originally posted by Xtasy0

the long sides arent straight in either picture.

they're angles, the first image the top side is slightly concave, in the second image the top is convex, when you overlay them you can see a gap ontop that is the same area as the missing block in the second image

This is the right exlanation, all props to you Xtasy.. And no, i didn't see it myself but I've seen that thing before and i've read that that is the reason. I see it now...

R

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