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Math Help - Related rates of change

  1. #1
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    Related rates of change

    Hi there, I am asked this scenario:

    The sides of an equilateral triangle are decreasing at a rate of da/dt=-(root6) cm. Find the rate of change of:

    a) The area of the triangle
    b) The height

    I have drawn a diagram but I don't know how to go on about solving these problems

    So i Know that for a) I'm meant to find da/dt
    b) dh/dt

    But I don't know to do arrive at the answer...please help.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by notamaths_geniuszz View Post
    Hi there, I am asked this scenario:

    The sides of an equilateral triangle are decreasing at a rate of da/dt=-(root6) cm. Find the rate of change of:

    a) The area of the triangle
    b) The height

    I have drawn a diagram but I don't know how to go on about solving these problems

    So i Know that for a) I'm meant to find da/dt
    b) dh/dt

    But I don't know to do arrive at the answer...please help.
    ok, first of all, what is the formula for the area and height in term of the side length?
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  3. #3
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    Well the Area of a triangle is A=1/2*b*a
    Three sides are the same so it is lets say: a
    And the perpendicular height is lets say: h

    A=1/2*a*h
    I know it has something to do with pythagoras but I can't seem to get it after that.
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by notamaths_geniuszz View Post
    Well the Area of a triangle is A=1/2*b*a
    Three sides are the same so it is lets say: a
    And the perpendicular height is lets say: h

    A=1/2*a*h
    I know it has something to do with pythagoras but I can't seem to get it after that.
    Note that the area of an equilateral triangle is A=\frac{\sqrt{3}}{4}s^2, and the height of the triangle is defined as h=\frac{\sqrt{3}}{2}s, where s is the length of the side.

    Can you take it from here?

    --Chris
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  5. #5
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    For a) A=root(3)/4 * s^2
    So I'm trying to find Da/Dt
    So the related rate of change is

    dA/dt=DA/Da * Da/dt

    Diff A=root(30)/4 * s^2 would give root(3)/2 *s

    so this is what it would look like
    DA/dt=root(3)/2 * s * -root(6)
    So far is this right and how would i find that missing side length of s.
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  6. #6
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by notamaths_geniuszz View Post
    For a) A=root(3)/4 * s^2
    So I'm trying to find Da/Dt
    So the related rate of change is

    dA/dt=DA/Da * Da/dt

    Diff A=root(30)/4 * s^2 would give root(3)/2 *s

    so this is what it would look like
    DA/dt=root(3)/2 * s * -root(6)
    So far is this right and how would i find that missing side length of s.
    All of this looks right. I guess this would be the rate of change of the area, for any equilateral triangle with a side of length s [s is arbitrary].

    --Chris
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