The radius of the base after rotating the rectangle will be 5
Since it has a perimeter of 32 units and it is to be rotated about the line, the solid to be created is a cylinder.
Let's calculate its radius from the perimeter;
[tex]2p=32[/tex]
[tex]2(b+h)=32[/tex]
[tex]b+h=16[/tex]
[tex]b=16-h[/tex]
Also, [tex]bh=60[/tex]
Thus;
[tex]h(16-h)=60[/tex]
[tex]h^2-16h+60=0[/tex]
Using the online quadratic formula, we have h = 6
Thus; b = 16 - 6 = 10
Since the line of rotation is the center, and the radius is half the line segment of the basis, then the radius is 10/2 = 5.
Thus the radius of the base after rotating the rectangle will be 5
To know more about rectangles follow
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