I perform not understand what I must start by doing. Could you please help me to start resolving this problem, offer me a hints or two?

This link talks around something related, but I perform not really know what they room talking about (probably beacause i haven"t read sufficient ptcouncil.net).

NOTE: I only want hints or a start of addressing this problem.

You are watching: Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral

Thanks a lot.


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Start through inserting a name: coordinates system.Now assume a point on the lines wherein the corners will certainly be. Let"s speak to the point $p$. Now figure out a way to create $p$ together a function of coordinates which follows the triangle political parties (a hint might be the equation the a line which friend probably have actually learned about).Express the area as a role of the edge coordinate discovered in 3.Try and also find a way to calculate the maximum of the area function.
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There is a organize that states that if you have a allude on the border of an it is intended triangle, climate the amount of the projections of the suggest to the other two sides remains constant. Use that theorem and the MA-MG inequality.


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Fold the triangle follow me the edges of the rectangle (three folds). This way, the three little triangle components will constantly cover the rectangle (you need to display this, of course). But if you study this covering, there is one rectangle that is just barely covered by the triangles v no overlap between the triangles and no parts of the triangles external the rectangle.

This method that this rectangle has actually an area which is half that of the large triangle and that that is plainly optimal (for any kind of other rectangle, the 3 triangles have an ext total area 보다 the rectangle, quite than equal).


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