Calculus: Optimization [Rectangle Inscribed in a Triangle]

About finding the rectangle of maximum area that can be inscribed in a 3-4-5 triangle. Why wouldn't you want to inscribe a rectangle in a triangle???

[@oliwierg5201]

Hi, can I also use somehow modified version of this method in equilateral triangle?

[@mr.murraysmathland381]

Yes - in fact, it's even a bit easier, as with equilateral triangles, since all 3 angles are 60 degrees, when you inscribe a rectangle (90 degree angles), it creates some 30-60-90 special right triangles, so the sides have the famous x - x rt(3) - 2x relationship!

[@oliwierg5201]

@@mr.murraysmathland381 Thank you so much