rectangle and semicircle

• Jun 23rd 2009, 10:17 PM
furor celtica
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?
• Jun 23rd 2009, 10:40 PM
Chris L T521
Quote:

Originally Posted by furor celtica
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.