Can someone solve this? How come after rearranging the blocks there is an empty square?
Area of a Triangle
- Thread starter Jin1976
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The area of the "empty" square in the second diagram is taken up by the top lines of the re-arranged triangle. The smaller red and green triangles have different slopes. If you look closely you'll see that line of the overall triangle is just a tad higher which accounts for the space of the "empty" square.
Hypotenuse is not straight.
Hugh said:
Going off of that the triangles are appearing to be correct in size but look at the hypotenuse and the area that it fills up within each empty block as it traverses up to the final point. The 'white space' that the triangle fills is extremely tiny, (in comparison to the first triangle) but it is evident. I bet if you were to take the area that the triangle filled in each of those blocks (the really small amount), the sum would probably be equivalent to that empty space within the triangle.
hope i explained that ok... (i may have just re-explained what he said.. haha)
x
Posts are all correct. The slope of the dark green triangle and the red triangle are different. Looking at the dark green triangle, you can see the slope of the triangles longest side is 5 across and 2 high. Then looking at the slope of the dark green triangle, counting 5 squares across, the slope rises more that 2 squares.
In actuality, the upper figure has 4 sides...not three. So it's not a triangle.
Nice brain teaser. Thanks for sharing.
In actuality, the upper figure has 4 sides...not three. So it's not a triangle.
Nice brain teaser. Thanks for sharing.
Shaun Ray said:
Nice explaination, I only need to make one correction. The second image actually has seven sides. :biggrin:
Shouldn't it be 8 sides since the "hypotenuse" is not a single line (i.e. two distinct sides across the top of the "hypotenuse" of the "triangle")?steveny said:
redshift said:
Hmmm....the two triangles that make up the hypotenuse actually form one continuous line without a change in the line angle. Therefore, I don't think there are 8 sides to the outer dimension of the diagram. :wink:
Actually, they don't form one continuous line... they definitely have different angles... the angle formed where they meet is not 180 degrees... it a slightly less... :wink:DocL said:
redshift said:
I have to respecfully disagree. I looked at the second hypotenuse while wearing my surgical loupes, held a straight edge ruler up to my screen, and it looks like a continuous straight line without a kink in it. :biggrin:
I can assure you that they are different angles. As somebody earlier noted, the two triangles have different slopes (i.e. different angles adjacent to the hypotenuse). Just count the squares. Start at the green triangle and count from the bottom left (2 squares up, 5 across). Now do the same for the red one - if you count 2 squares up and 5 across you won't end up on the line - it will be slightly off. So while the angle may appear to be 180 degrees where the two hypotenuse(es) meet, it is definitely not. :biggrin:DocL said:
redshift said:
I guess I need to get my checked again. :smile:
none of the big triangle is actually a triangle because the hypotenuse is not straight.
(tan θ1 = 3/8) which does not equal to (tan θ2 = 2/5) so θ1 and θ2 is not the same angle so the long line is not straight line.
If the red triangle is at 7.5 square instead of 8 at the base then it would be a straight line :smile:
(tan θ1 = 3/8) which does not equal to (tan θ2 = 2/5) so θ1 and θ2 is not the same angle so the long line is not straight line.
If the red triangle is at 7.5 square instead of 8 at the base then it would be a straight line :smile:
exactly. :biggrin:AndyH said:
And I thought I had one of the easiest jobs in the world.
