a door is in the shape of a rectangle surmounted by a semicircle whose diameter is equal to the width of the rectangle. if the perimeter of the door is 7 m, and the radius of the circle is r metres, express the height of the rectangle in terms of r
i found pretty easily h = 0.5 (7 - 4r - pi x r)
but the answer says 2r, not 4r. who is a making a mistake here? w = 2r right?

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...and that put an end to Flannigan's ball.

The width is 2r, but you don't consider both sides of the rectangle of width 2r in calculating the perimeter!! You just calculate perimeter = width + 2*height + length of semicircle arc.

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