Putting rectangles into circles

Part IV Taking the Shape of Geometric Word Problems 

Just how large a rectangle will fit into a circle, if you have some particular constraints  

The Problem You want to fit a rectangle with length 8 inches into a circle with radius 5 inches. What width will the rectangle have if each of the vertices of the rectangle are to be on the circle  

A rectangle measuring 8 by 6 inches has an area of 48 square inches. A rectangle with these dimensions is not the largest rectangle that you can fit into a circle with a radius of 5 inches. In calculus, you prove that the largest rectangle that fits into a circle is really a square. So, if that s the case, what size square fits into a particular circle  

The Problem What is the length of any side of a square that fits into a circle whose radius is 5 inches  

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