A norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the largest possible Norman Window with a perimeter of 46 feet?
2006-11-02 03:35:34 · 5 answers · asked by wasatchjeeper 2 in Science & Mathematics ➔ Mathematics
D = W
P = Pi*D/2 + 2(W+L) = 46 ft
3.14*W/2 + 2(W + L) = 46
(3.14/2 + 2)W + 2L = 46
3.57 W + 2L = 46
L = (46 - 3.57W)/2
2006-11-02 03:58:12 · answer #1 · answered by Anonymous · 0⤊ 0⤋
62
2006-11-03 20:58:01 · answer #2 · answered by ali a 1 · 0⤊ 0⤋
3x+pi(x/2)=46
x=10.0638918716 feet (width of window)
Assuming that the rectangle would have to be a square.
2006-11-02 11:57:46 · answer #3 · answered by Anonymous · 0⤊ 1⤋
perimeter=2h+w+pi*w
46=2h+w(1+pi)
w=(46-2h)/(1+pi)
area=hw+piw^2/4
=(h/(1+pi))[46-2h]+(pi/4)[*(46-2h)^2/(1+pi)^2]
differentiate and equate to 0 and solve for h
substituting you get w
2006-11-02 11:42:34 · answer #4 · answered by raj 7 · 0⤊ 0⤋
rfamilime:
perimeter=2h+w+ (pi*w/2) !!!
(half a circle only)
2006-11-02 12:02:06 · answer #5 · answered by just "JR" 7 · 0⤊ 0⤋