Yahoo Answers: Answers and Comments for Math ratio [數學]
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Sun, 10 Oct 2010 08:11:22 +0000
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Yahoo Answers: Answers and Comments for Math ratio [數學]
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From Godfrey: Let the length be L and width be W
Original l...
https://hk.answers.yahoo.com/question/index?qid=20101010000051KK00234
https://hk.answers.yahoo.com/question/index?qid=20101010000051KK00234
Sun, 10 Oct 2010 09:27:20 +0000
Let the length be L and width be W
Original length length of small rectangle
 = 
Original width width of small rectangle
length of small rectangle = W
width of small rectangle = L –W
L/W = W/(L – W)
L(L – W) = W^2
L^2 –LW = W^2
We want to find the ratio W to L
Let W = 1
L^2 –L(1) = (1)^2
L^2 – L = 1
L^2 – L – 1 = 0
This is quadratic Equation
Using quadratic formula, solve for L
L = [b+(b^2 – 4ac)^0.5]/2a
a = 1, b = 1, c = 1
L= [(1)+((1)^2  4(1)(1))^0.5]/2(1)
L= [+1)+(5^0.5]/2
Ratio L/W
[+1)+(5^0.5]/2 /1
(1+5^0.5)/2