Puzzle time - the Triangle
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A teacher (lets call him Klaus) used to give this problem as part of his elementary geometry class:
A right triangle has hypotenuse (BC) of length 10, and a height (AP) of length 6. What is the area?
His average students (lets call them Horace and Ax) got full credit for the answer 1/2 * 10 * 6 = 30.
But a really smart kid (lets call her Taiwan girl) couldn’t solve the problem.
Why not?
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Nope that was just a typo on my part when I went back to clarify!
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I was trying to say that the “really smart” kid cannot solve the problem because of the ambiguity stemming from there having three possible right triangles in the diagram: ABC, ACP, ABP. So when you say something like the hypothenuse has length 10, it’s ambiguous whether you’re referring to which hypothenuse, AB, AC, or BC.
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Too lazy to look up the required formulas right now, but with A fixed as a right angle and CB equal to 10, height AP will be confined to a certain range. I guess it's at its maximum when angles C and B are both 45 degrees and even then AP will likely be less than 6? If that's the case, the scenario is simply impossible.
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I should have named the smart kid Nunatax.
The triangle is impossible as this simple diagram shows us:
(Recall that, if the angle CAB is a right angle, it must lie on the perimeter of the circle, per Euclid
The maximum height of AP is 5.
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@jon-nyc said in Puzzle time - the Triangle:
I should have named the smart kid Nunatax.
Correct, you should not have picked me! 555
