I carry out not know what I must start by doing. Can you please assist me come start fixing this problem, provide me a hint or two?

This attach talks around something related, yet I execute not really understand what they space talking about (probably beacause ns haven"t read enough brickandmortarphilly.com).

NOTE: I just want ideas or a start of fixing this problem.

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

Thanks a lot.


Start by inserting a coordinate system.Now assume a allude on the lines whereby the corners will certainly be. Let"s speak to the allude $p$. Now number out a way to write $p$ as a role of works with which follows the triangle sides (a hint could be the equation that a heat which you probably have actually learned about).Express the area together a duty of the edge coordinate uncovered in 3.Try and also find a method to calculate the maximum of the area function.

There is a organize that says that if you have a suggest on the border of an equilateral triangle, then the sum of the projections the the suggest to the other two sides remains constant. Usage that theorem and the MA-MG inequality.


Fold the triangle along the edge of the rectangle (three folds). This way, the three little triangle parts will always cover the rectangle (you need to display this, of course). But if you study this covering, over there is one rectangle that is simply barely spanned by the triangles v no overlap in between the triangles and also no parts of the triangles exterior the rectangle.

This way that this rectangle has actually an area which is half that that the huge triangle and also that it is clearly optimal (for any type of other rectangle, the three triangles have more total area than the rectangle, quite than equal).


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