Fidn the dimensions of the rectangle of maximum area that can be inscribed in a circle of radius 6cm

Question

anonymous · Answer

@ganeshie8

anonymous · Answer

you're looking for the area of a square with a diagonal length of 12. |dw:1433820528039:dw|

anonymous · Answer

ok how would i start , use both areas?

anonymous · Answer

@Zarkon

anonymous · Answer

Calculus?

anonymous · Answer

yes

anonymous · Answer

@hartnn

anonymous · Answer

Well, peach was correct about what type of figure you'd need, but I assume you have to show it, lol. 

Okay, so optimization. We need a way to relate information about the circle with the rectangle inscribed in it. So we need the formula for what we want to optimize, which is the area of a rectangle.

Area of rectangle = LW

Next we want some known value of the circle, whether it be from a formula or just one of its dimensions, that we can somehow relate to the length and width of the rectangle. 

So we know the radius of the circle is 6. Which means the diameter of the circle is 12. Can you think of a way to relate the radius or diameter of the circle to the length or width of the rectangle?

anonymous · Answer

um one side of rectanlge is 12cm long ?

anonymous · Answer

Well, that wouldnt be possible actually. 12 is the length of the diameter, which is the maximum length of any line segment inside of the circle. All of the lengths of the rectangle would need to be less than 12. But think about it from a drawing

|dw:1433822104287:dw|

No matter what type of rectangle I draw inscribed in a circle, I can draw a diameter that will always be equal to the diagonal across that rectangle. So the length of the diagonal of the rectangle is 12, which is equal to the diameter of the circle. Can you think of a formula that solves for that diagonal?