Optimization question: Find the dimensions of a rectangle of largest area that can be inscribed in the circle x^2 + y^2=9

Question

anonymous · Answer

what is the area?

amistre64 · Answer

its a square.... just to let you know ;)

anonymous · Answer

can you please help me out and tell me how to get the solution?

amistre64 · Answer

the solution to this is to just use 1/4 of the circle  the part that lies in the first qudrant

amistre64 · Answer

we know the are of the 'rectangle' = xy right?  and our 'line' is full of x and y options; so lets use the equation to define x or y in terms of the other...

anonymous · Answer

yes i got y= square root of 9-x^2

amistre64 · Answer

x^2 + y^2 = 9

x^2 = 9 - y^2

x = sqrt(9-y^2) ; use this value of 'x' in the rectangle area equation

amistre64 · Answer

y = ... is fine to; doesnt matter lol

anonymous · Answer

lol okay then just substitute inside the equation A=xy

amistre64 · Answer

yes; then derive :)

anonymous · Answer

okay thank you so much

amistre64 · Answer

just to let you know; the optimum is at 45 degrees; or rather when y = 9sin(45) :)

anonymous · Answer

okay thank you