Area of hexagon is maximum while perimeter is fixed

[nmr]

this is the given problem:

and this is my attempt at a solution:

I am stuck here as the variable y is unknown and I want to express y in terms of x, but cannot figure out how to do so.
Thanks for any help!

 

[Ray Vickson]

this is the given problem:

View attachment 73096

and this is my attempt at a solution:

View attachment 73097

I am stuck here as the variable y is unknown and I want to express y in terms of x, but cannot figure out how to do so.
Thanks for any help!

Do not post thumbnails. Please read the 'pinned' thread 'Guidelines for students and helpers', which explains the reasons for this policy.

 

[Mentallic]

You're told that the perimeter is fixed, which means that P is some constant. You can represent y in terms of P and x so that you then have the area A in terms of just one variable x.

 

[nmr]

I got it, thanks a lot!

Also sorry for not reading the posting guidelines beforehand.