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> The hypotenuse of a right-angled triangle (in a standard American examination) is 10 inches, the altitude dropped onto it is 6 inches. Find the area of the tr
by rdtsc 5y ago
> The hypotenuse of a right-angled triangle (in a standard American examination) is 10 inches, the altitude dropped onto it is 6 inches. Find the area of the triangle. American school students had been coping successfully with this problem over a decade. But then Russian school students arrived from Moscow, and none of them was able to solve it as had their American peers (giving 30 square inches as the answer). Why?
That's a good one. I know the answer but won't reveal it since it's a fun one to discover yourself.
- laszlokorte 5y agoFunny in germany we learn the formular for just that: Area_triangle = Base_triangle * Height_triangle / 2 /edit: fixed factor of two
- hereforphone 5y agolol?
- blagie 5y agoThere's a funny story. Before PISA, Finland looked up to the German school system, which was clearly considered superior by both sides. When PISA came out in 2000, Finland was surprised to come out on top for Europe. Germany's performance in math was abysmal -- behind the US even. People started flocking to see what Finland did, and stopped looking up to Germany. https://nces.ed.gov/pubs2002/2002116.pdf https://nces.ed.gov/pubs2002/2002116.pdf The German school system has since gradually improved -- it's no longer behind the US -- but it's far from world-leading.
- Someone 5y agoThat’s either a nice example of hemibel thinking (http://libertycorner.blogspot.com/2004/07/hemibel-thinking.html http://libertycorner.blogspot.com/2004/07/hemibel-thinking.h...), of your memory going away, or of an extremely lousy education. (You are of by a factor of 2)
- satchlj 5y agoI'm not sure sure if you made a mistake or if you are joking
- lordnacho 5y agoThe problem is exactly that the application of a formula requires some assumptions to be met, the first of which is logical consistency. Try to draw a triangle such as the one mentioned.
- blagie 5y agoWell, there's many possible answers. I'll give a few: - Russia doesn't have "inches" - The question has English terms like "hypotenuse" - The Russian students were younger - There were differences in conventions, e.g. which side is down. An altitude dropped onto the hypotenuse of a right triangle could be perpendicular, or either of the two other sides. - And so on... A lot of these problems are designed for a conversation rather than a solution.
- rdtsc 5y agoInches is not the issue. It could be any units. The joke about the American vs Russian students was a jab at the American students, not the Russian ones! Something about the Russian students seeing something that American student couldn't. I don't agree with the premise of course, just providing the extra info as a hint. I can believe, however, that this problem was on a standardized test in US at some point. This last sentence points to the answer a bit more too :)
- mhh__ 5y agohttps://en.m.wikipedia.org/wiki/Altitude_(triangle) https://en.m.wikipedia.org/wiki/Altitude_(triangle) for reference, I guessed what the issue was but wasn't familiar with the term altitude
- kccqzy 5y agoExactly. In grade school the formula being taught was "base times height over 2" but no one mentioned the term altitude.
- culebron21 5y agoProbably, I'm too proficient in English to see the problem. * guess #1: they read it as a Pythagoras triangle, with sides 10, 6 and 8, hence they answered 6 * 8 / 2 = 24. * guess #2: they could not make sense of "altitude dropped onto it". * they tried to convert units and forgot that for area, the coefficient is squared?
- thaumasiotes 5y agoThe problem is that right triangles have to obey a constraint. The angle opposite the hypotenuse is 90 degrees. Thus, once you've fixed the two endpoints of the hypotenuse, not all points are eligible to be the final point of the triangle. All other points in space can form a triangle with those two points, but it may not be a right triangle. If you interpret the hypotenuse as the diameter of a circle, all -- and only -- the points on the circle, except the hypotenuse's endpoints, will form a right triangle with the hypotenuse. If the diameter's length is, as specified in the problem, 10 inches, this tells us that the circle has radius 5 inches. This is the maximum distance between the hypotenuse and the third corner of the triangle. The problem tells us that the distance from the hypotenuse to the third corner is 6 inches, which is impossible.
- Koshkin 5y ago> which is impossible Or, generally, is only possible in a non-Euclidean geometry (which the Russian students apparently did not know very well).
- chaosmachine 5y agoSince none of the replies so far have it correct, here's a spoiler: https://math.stackexchange.com/questions/1594740/v-i-arnold-says-russian-students-cant-solve-this-problem-but-american-student https://math.stackexchange.com/questions/1594740/v-i-arnold-...
- rdtsc 5y agoFair enough. I was going to wait a bit longer to provide the hint. I do like that there are non-Euclidian answers. However, I doubt non-Euclidian geometry was expected on standardized tests tests in US, if the anecdote is to be believed that this came from say SAT or ACT.
- cperciva 5y agoClearly the problem was too complex for the Russian students.
- cperciva 5y agoSince this is being downvoted, maybe I should elaborate that it was unreal?
- scotty79 5y agoSPOILER: Well my answer but it's a correct one. ˙ʇsǝʇ ǝɥʇ uo „ǝlƃuɐıɹʇ ɥɔns ou s,ǝɹǝɥʇ„ ɹǝʍsuɐ ou sɐʍ ǝɹǝɥʇ ǝsnɐɔǝq ʇı ǝʌlos ʇ,uplnoɔ sʇuǝpnʇs uɐıssnᴚ ssǝnƃ I ˙lɐnbǝ ǝɹɐ sǝƃpǝ ɹǝɥʇo oʍʇ uǝɥʍ s,ʇI ˙ގ ʇsoɯ ʇɐ ǝq plnoɔ ʇı uo pǝddoɹp ǝpnʇıʇlɐ ǝɥʇ 0⇂ ǝsnuǝʇodʎɥ ɥʇıʍ uǝɥʇ ǝlƃuɐıɹʇ pǝlƃuɐ-ʇɥƃıɹ ɐ s,ʇı ɟI
- deleted 5y ago[deleted]