Question 996106
Done part-way through but not including the derivative & maximization work:


Draw a triangle, base x, height h, the two equal sides each d.  Cut x exactly in half forming two of {{{x/2}}}.


The drawing allows you to first form two equations.
{{{system(2d+x=3,(x/2)^2+h^2=d^2)}}}


Starting with perimeter equation solve for d in terms of x.
This part will be {{{d=(1/2)(3-x)}}}.


Substitute this formula for d into the pythagorean relation ship equation and solve for h:


{{{(x/2)^2+h^2=((1/2)(3-x))^2}}}
{{{h^2=(1/2)^2*(3-x)^2-(x/2)^2}}}
{{{h^2=(1/4)((3-x)^2-x^2)}}}
{{{h=(1/2)sqrt(9-6x+x^2-x^2)}}}
{{{highlight_green(h=(1/2)sqrt(9-6x))}}}


A(x) will be the area function.
{{{A(x)=(1/2)x*h}}}, and now you have a formula for h.
{{{highlight_green(A(x)=(1/2)x*sqrt(9-6x))}}}


Omitting the differentiation steps but starting with the product rule, I am finding {{{dA/dx=(9-9x)/(4sqrt(9-6x))}}}; and you can continue the maximization process...