College Algebra/Geometry
posted by Fred .
What size should be the frame be?
Suppose an artist has a circular picture with a diameter 6 inches which she wishes to frame by a uniform width frame with covers 1/2 inch width uniformity of the painting and has total area equal to that of the exposed painted surface when the frame is in place.

Is there a question here?

What size should the frame be?

if the frame is width w, then it covers 1/2 inch of painting plus w outside the painting.
pi(3.5)^2 = pi((3+w)^2  (3^22.5^2))
25/4 = w^2 + 6w + 9  (925/4)
w^2 + 6w = 0
solve that for w, and you get w=0
so, the border is just 1/2 inch wide, and does not extend outside the painting.