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optimization
a person determined the length of a pipe they could safely carry around a hallway corner was 26 feet. they were wrong and now the pipe is stuck with one end exactly 10 feet from the corner. determine the dimensions of the largest rectangle which is formed. the largest rectangle is the one with the largest area.
picture is attached.
thanks

I will assume the width of the pipe is negligible. Otherwise, the problem is more difficult.
See that little triangle in the upper corner where 10 is the dimension?.
It's hypoteneuse(that section of pipe) can be represented by
$\displaystyle \sqrt{(10x)^{2}+x^{2}}$
It that a start?.