# How do you find the dimensions of the rectangle with largest area that can be inscribed in a semicircle of radius #r# ?

The dimensions of the rectangle is

The equation of the semicircle is

The area of the rectangle is

The critical points are when

That is

Then,

The maximum area is

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To find the dimensions of the rectangle with the largest area inscribed in a semicircle of radius ( r ), the length of the rectangle should be twice the radius of the semicircle, and the width should be equal to the radius of the semicircle. Therefore, the dimensions of the rectangle are ( 2r ) for the length and ( r ) for the width.

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