Monday, April 09, 2018

geometry problem fo' yo' ass

Here ya' go:


I wasn't able to solve this, but according to this video (click the link to see the solution; I watched the vid, so I now know the answer), a few Chinese 5th-graders solved the problem in under a minute. That in itself is a hint, by the way. If you solve the problem, leave your answer in the comments, and please show your work/reasoning.



3 comments:

  1. I've gotten more stupid as I age. I could follow the explanation, but I doubt that the reputed Chinese fifth graders used the method shown. I suspect that if they did it in less than a minute, they didn't go through the formal methods shown.

    Bill

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  2. I was thinking something similar. The only way to solve the problem in under a minute is to have (recently) memorized the specific geometric properties relevant to this particular problem. So I suspect that the math students had just done a unit on triangles and parallelograms and had this "quickie" method fresh in their minds.

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  3. Fast way, it took me more than one minute, but less than 10. And I am almost 63.
    Label all of the areas NOT in yellow:
    a = the red area
    b = the area below that
    c = the area to the right of the red area
    d = the area below 79
    e = the area below 72
    f = the area to right of 72
    g = the area below 10
    (It takes a lot longer to explain it than to label it.)
    Now, use the triangle formulas A = 1/2(b + h). Also, for a parallelogram, the length of top = length of bottom, and
    length of right = length of left
    If you go horizontally across the figure,
    there are 2 triangles whose bases are part of the top and 2 triangle whose bases are part of the bottom. The heights are the same.
    So (a + b) + (72 + e + 8) = (c + 79 + d) + (f + 10 + g)
    if you go vertically, there is one triangle whose base is the left side and two triangle whose base is the right side. Again, the heights are the same.
    So (a + c + 72 + f) + (d + 8 + g) = (b + 79 + e + 10)
    And, amazingly, all of the letters cancel out except a, the red area.
    a = 9


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