(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Each edge of a square has length L. Prove that among all squares inscribed in the given square, the one of minimum area has edges of length [tex]\frac{1}{2}L\sqrt{2}[/tex]

2. Relevant equations

3. The attempt at a solution

I started by drawing a square of sides L. Then labeled the vertices: (0,0) (L,0) (0,L) (L,L) then drew an inscribed square with variable x and the vertices were: (x,0) (L,x) (L-x,L) (0,L-x)

Then from this I set the distance of all the lines between each of these inscribed triangles vertices equal to one anotehr, to determine what values of X would work for the equation.

I determined that x=x. Is this true? Could you rotate a square 360 degrees while still being inscribed within a square?

I was stumped at this part, but if it's true. Then area of the inscribed square is going to be the distance of one of the inscribed squares length squared.

such as.. [tex]((x-L)^{2}+(x)^{2})^{2}[/tex]

Then i would take a derivative of this and determine the minimum point?

Is this right?

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# Homework Help: Optimization: square inscribed in a square

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