Physics

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An equilateral triangle initially has side length equal to 17 cm. Each vertex begins moving in a straight line towards the midpoint of the opposite side at a constant rate of 2.3 cm/s, continuously forming progressively smaller equilateral triangles until it disappears. At what rate is the area of the triangle decreasing at the instant it vanishes? The area A of an equilateral triangle with side length s is

A= (sqrt(3)/4)(s^2)

  • Physics -

    dA/ds = sqrt 3 (1/2) s

    dA/dt = .5 sqrt 3 sds/dt
    but
    altitude h = (s/2) sqrt 3
    dh/dt = .5 sqrt 3 ds/dt
    so
    ds/dt = [2/sqrt 3] dh/dt

    dA/dt=.5 sqrt 3*[2/sqrt 3]s dh/dt
    = s dh/dt
    evaluate when s = 17 and dh/dt = -2.3

  • whoa -

    whoa, at the instant it vanished?

    dA/dt = s dh/dt
    as s ---> 0 and dh/dt is constant
    dA/dt ---> 0

  • Physics -

    wow got to right the question and solution down

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