Determine the dimensions of the rectangle of largest area that can be inscribed in a semicircle of radius 3. .. Not sure how to do

Question

anonymous · Answer

got a picture? it would help to use that the equation of a circle with radius 3 is 
$$x^2+y^2=9$$ and so the upper half would be 
$$y=\sqrt{9-x^2}$$

anonymous · Answer

|dw:1322537648747:dw|

anonymous · Answer

Well there is a picture but not exactly sure how that would help. The rectangle is in a circle with radius 3. Thats about it. need to find the largest the rectangle can be

anonymous · Answer

yeah like yours. And from the origin to x is 3, then W and l for the height and length

anonymous · Answer

so area of that rectangle i drew is 
$$2x\times \sqrt{9-x^2}$$ since the base is 2x and the height is 
$$\sqrt{9-x^2}$$ so find the maximum value of the area function 
$$A(x)=2x\sqrt{9-x^2}$$  i.e. take the derivative, find critical points etc

anonymous · Answer

Yeah I am not sure if I see it. Dont get how we found the Area to be what you got. I thought it would be just (height)*(width) so would be (x)($$\sqrt{9-x^2}$$

zarkon · Answer

it is (height)*(width)

the width is 2x