What is the area of the largest equilateral triangle which fits inside a square of side a?
so area of trinagle is $\frac{a^2}{2}$, however it is wrong, why ?
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1That's not an equilateral triangle, for one thing. – Dan Uznanski Jan 27 '17 at 18:43
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1The largest triangle is indeed half the area of the square. But the largest equilateral triangle will be something smaller than that. – Doug M Jan 27 '17 at 18:43
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just get a piece of paper and draw a few pictures. This is a very visual problem. – Will Jagy Jan 27 '17 at 18:48
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You shouldn't consider the height and the base to be equal, that is why the area isn't $\frac{a^2}{2}$ – Seyed Jan 27 '17 at 18:49
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This provides an answer for triangles in general. – Watson Jan 27 '17 at 18:56
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@Arnaldo this is the question – user408113 Jan 27 '17 at 20:36
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@arnaldo i drew the same thing as below however i do not know hwo to proceed – user408113 Jan 27 '17 at 20:37
2 Answers
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Hint. Place one vertex of the triangle on one of the corners of the square, and the other two vertices symmetrically placed on the opposite neighbouring sides of the square
David Quinn
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Lanel the side of the triangle $x$ and use some basic trigonometry and Pythagoras to make an equation for $x$ – David Quinn Jan 27 '17 at 21:01
