aria triunghiului dreptunghic [tex]A= \frac{x*y}{2} \\ x*y=16;y= \frac{16}{x} [/tex]
aria cercului [tex] A_{c}= \pi R^2;R= \frac{ipotenuza}{2};R= \frac{x^2+y^2}{2}= \frac{x^2+ \frac{256}{x^2} }{2} \\ [/tex]
R'(x)=[tex] \frac{2x- \frac{256*2}{x^3} }{2} [/tex]
R'(x)=0
[tex]2x^4-512=0 \\ x^4=256 \\ x=4;y=4[/tex]
ipotenuza =[tex] \sqrt{4^2+4^2}=4 \sqrt{2} [/tex]
R=[tex] \frac{4 \sqrt{2} }{2} =2 \sqrt{2} [/tex]
[tex] A_{c}= \pi *(2 \sqrt{2})^2=8 \pi [/tex]