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 ?
Largest equilateral triangle which fits inside a square
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$\begingroup$
algebra-precalculus
geometry
optimization
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1That's not an equilateral triangle, for one thing. – 2017-01-27
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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. – 2017-01-27
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0just get a piece of paper and draw a few pictures. This is a very visual problem. – 2017-01-27
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0You shouldn't consider the height and the base to be equal, that is why the area isn't $\frac{a^2}{2}$ – 2017-01-27
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0[This](http://math.stackexchange.com/questions/1028600) provides an answer for triangles in general. – 2017-01-27
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0@Arnaldo this is the question – 2017-01-27
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0@arnaldo i drew the same thing as below however i do not know hwo to proceed – 2017-01-27
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
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0ok what do i do after???????? – 2017-01-27
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0what do i do do do – 2017-01-27
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0Lanel the side of the triangle $x$ and use some basic trigonometry and Pythagoras to make an equation for $x$ – 2017-01-27
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