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Math Help - rectangle and semicircle

  1. #1
    Senior Member furor celtica's Avatar
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    rectangle and semicircle

    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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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by furor celtica View Post
    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?
    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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