I perform not recognize what I must start through doing. Could you please help me to start fixing this problem, offer me a hints or two?

This attach talks around something related, yet I execute not really recognize what they space talking about (probably beacause i haven"t read enough aramuseum.org).

**NOTE**: I just want clues or a begin of addressing this problem.

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

Thanks a lot.

Start by inserting a coordinate system.Now assume a allude on the lines where the corners will be. Let"s contact the allude $p$. Now number out a means to create $p$ as a function of coordinates which complies with the triangle sides (a hint could be the equation that a line which you probably have learned about).Express the area as a function of the corner coordinate uncovered in 3.Try and find a method to calculate the maximum of the area function.

There is a organize that states that if you have actually a suggest on the border of an it is intended triangle, then the amount of the projections that the point to the other two sides stays constant. Usage that theorem and the MA-MG inequality.

Fold the triangle follow me the edge of the rectangle (three folds). This way, the three small triangle components will constantly cover the rectangle (you need to display this, that course). Yet if you study this covering, over there is one rectangle the is simply barely covered by the triangles with no overlap between the triangles and also no parts of the triangles outside the rectangle.

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

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