This Defies Everything!!!!!!!!!
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krogoth
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Pressure
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
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
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krogoth
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the area of the smaller shapes never changed 
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Can someone make one final summary of how we've actually solved this, because I'm still confused. It's nothing to do with discrepencies between the hyps' cos I did a technical drawing of it in Microsoft Visio without any discrepancies and we're still left with a gap.
ValVed RaY
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Yeah so easy to figure out after you read the solution posted by someone else.
p.s. you don't sound very smart
/me gives out prize to pressure
:cheers:
:cheers:
Reaper978
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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.
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krogoth
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none of u used trigs
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krogoth
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it's meant for u to realize that just because two triangles have same angles and only 2 sides the same it doesn't mena that they are similar Edit: which demonstrates the trig definitions, whereis the vid...
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The hypos in the first post are clearly different but that's just someone's simple mistake when drawing it or a deliberate mistake to get your type of reaction and take you down the wrong path.
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.
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.
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CyberGeek
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I'll try to explain it (first post! Woohoo! Been registered for nearly a month ^_^.)
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 ^_^.
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 ^_^.
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gMANiac
Guest
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 straight line from the peak point at upper right down to the low point at lower left, it would create an area equal to the area that is "missing" from the second arrangement, which, BTW, creates the same obtuse angle in reverse, that is "filling" the area in the "missing" square.
I give up.
[edited for some wording that may be confusing]
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krogoth
Guest
lol use the trig definitions and it would be impossible for the two figures to share the same area
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brettt
Guest
Thank you Captain Obvious! :-p
Good lord, where do you people find this stuff?
Those shapes are not Triangles
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
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
Actually, now that I think about it, its not because the Hypt. isn't straight... Because looking at the slopes NEITHER is straight. So that's a moot point. That's not the correct answer. Neither picture is a Triangle.
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!
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!
mannyfresh027
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this is made using grid lines in photoshop and copy pasting
everything is snapped to the grids
i zoomed in, showing that the shapes could not possibly fit in the arrangement
everything is snapped to the grids
i zoomed in, showing that the shapes could not possibly fit in the arrangement
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krogoth
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so any chance u guys are passing the time for the vid?
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Stubbychubs
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This is too easy. The two triangles are not similar triangles, therefore the angles are different. The green triangle is 2 squares high and 5 squares long. If we assume the red triangle is similar to the green one, and that is 1.5 times the size of the green one, the height should be 3 squares, which it is, and 7.5 squares, which it is not. Problem solved.
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Xtasy0
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well the right answer was also on the first page of thise thread......twice....
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Stubbychubs
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Just read throught this whole thread. Looks like a some people have already answered it correctly
Ahnteis
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The problem is made difficult by the grid lines. You count the total length and total height of the shapes but you don't compare the actual shape.
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.
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.
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Mr. Freeman
Guest
Easy and short way to say it
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
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
It can't be *that* hard! I saw this exact same problem in a "Murderous Maths" book a few years ago... that book's written for young kids (8+ ?), and it didn't give an answer. Apparently the answer was scribbled out bt some evil guy and you had to work it out for yourself. I didn't even try to work it out though.
I didn't even try to work it out though.
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Guest
Guest
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...
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