math ratio

[匿名]

2010-10-10 4:11 pm

foolscap paper is such that cutting off a square whose sides equal to the shorter side of the paper leaves a rectangular which has the same shape as the original sheet. finf the ratio of the original page.

ans: (1+5^1/2)/2

can you show the steps to me??

回答 (1)

Godfrey

2010-10-10 5:27 pm

✔ 最佳答案

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

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