circle rectangle thing relation

R

red and white kop!

Junior Member
Joined
Jun 15, 2009
Messages
231
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?
 
Perimeter of rectangle : 2w+2L=7

2(2R)+2L=7

4R+2L=7

2L=7-4R

L=7/2-2R

This is how I done it, Do you agree with me ?

It will be better if you illustrate a drawing, because I know you would knew it.
 
red and white kop! said:
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?
Click to expand...

The book is correct

If the bottom of the door is included in the perimeter then:

width = 2r

P = 2L + W + ?r...... (the other width is taken up by the semi-circle)

P = 7 = 2h + 2r + ?r

h = 0.5*(7 - 2r - ?r)
 
red and white kop! said:
actually the door includes the semicircle, kinda like some strange hobbit door.
Click to expand...

Tolkien fan!!
 
ok the diameter of circle/width of rectangle is not included in the perimeter. stupid mistake.
feanor curufinwe
 
lookit Kop: "what's fact and what's fiction" in your darn problem? :shock:
 
You must log in or register to reply here.
Top