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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 Answer

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  • 10 years ago
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    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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