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January 12th, 2010 by admin | Filed under Brain Teasers, Math Tricks.I came across a very interesting problem – one that seems to involve math tricks of some sort. Or is it magic? Whatever it is, it is certainly a math brain teaser! Anyway, here is the graphic that had me scratching my head:
So what’s the deal here?? Where did the hole come from? Please post your answers :)
Tags: brain teaser, math brain teaser, Math Tricks
these are not triangles. if u all check carefully the hypotenuse of the figures, it is not actually a straight line. one can check on the first figure, consider the points (0,0), (8,3) and (13,5), by solving for the slope, they are not equal which should have been if they are collinear.so as the second figure by considering the points (0,0), (5,2) and (13,5).so rearranging them will not yield with the same area. i hope i did not confuse you
Additional to what Mr. Reydel explained above.
We will try to solve it in both ways, geometrically & arithmetically.
1st method:
- Print the Picture of these 2 “triangles”
- Use a fine pencil and a perfect ruler and reproduce “accurately” a straight hypotenuse for each of the 2 figures.
- You will notice that it’s not matching with the picture. In figure 1 there is a lost area and in figure 2 there is access of area. The sum of these areas will be equal to 1 square.
And that’s where this “additional” square came from
2nd method:
Since this mathematical trick is based on “area” illusion, let us calculate the area of the 2 triangles arithmetically:
Let us recall the formula of calculating the area of a triangle:
Triangle Area = ½(b×h)
Whereby b = base & h = vertical height
In our case b=13 squares (the horizontal side of the triangles)
h=5 squares (the vertical side of the triangles)
=> ½(13×5)= ½65=32.5
the triangles area should be 32.5 squares. But if we double check by counting the squares we will find that:
Figure 1 area = 32 square (less than 0.5 from the exact triangle shape)
Figure 2 area = 33 square (more than 0.5 from the exact triangle shape)
That’s equal to 1 full square. :D
Have a nice day
whats da answer plsssssssssssssssssssss from the author
This is actually an optical illusion. The hypotenuse is very slightly curved, such that it covers enough extra area to account for the “hole”.
The Dark Green and the Red Triangles’’ angles are different hence the two big “triangles” are not really Triangles. But for the naked eye the variation in gradient is not visible on the picture.
the 2 tiangle arent equal
there are 13 sqaures fully occupied by the length of the red and the green figures on the first triangle. On the 2nd triangle there is only 12 squares oocupied by the dark green, yellow, and green figures. That is how you got the HOLE.