# math ratio

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??

### 1 個解答

• 10 年前
最愛解答

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

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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