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).


*

Thanks for contributing solution to brickandmortarphilly.comematics ridge Exchange!

Please be certain to answer the question. Administer details and share your research!

But avoid

Asking because that help, clarification, or responding to other answers.Making statements based on opinion; ago them up with referrals or an individual experience.

Use brickandmortarphilly.comJax to style equations. Brickandmortarphilly.comJax reference.

See more: Dj Won T You Play This Girl A Love Song, Dj Play A Love Song

To find out more, watch our tips on writing an excellent answers.


write-up Your answer Discard

By click “Post her Answer”, you agree come our regards to service, privacy policy and also cookie policy


Not the prize you're feather for? Browse other questions tagged applications maxima-minima or questioning your own question.


*

site architecture / logo design © 2021 stack Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.10.8.40416


your privacy

By clicking “Accept every cookies”, girlfriend agree ridge Exchange can store cookies on your machine and disclose info in accordance with our Cookie Policy.