Calculus

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A fence 6 feet tall runs parallel to a tall building at a distance of 7 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?

  • Calculus -

    Have you considered drawing a sketch?

    let x be the distance from the fence to the ladder base, so x+7 is the distance to the building from the ladder base.

    x/6=(x+7)/h where height at the building intercept.

    dx/6=dx/h-7/h^2 dh -x/h^2 dh

    dx/dh (1/6-1/h)=-1/h^2 (7-x)

    but dx/dh=0 so

    x must 7

    so length can be figured from
    length=2(sqrt (16+49))

    check that, I did it quickly.

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