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Math Help - College geometry: Minumum and triangle problem

  1. #1
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    College geometry: Minumum and triangle problem

    Show that for a triangle with given area and given side, the sum of the other two sides is a minimum if and only if the triangle is isosceles.

    Thanks for your help.
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  2. #2
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    Quote Originally Posted by ordinalhigh View Post
    Show that for a triangle with given area and given side, the sum of the other two sides is a minimum if and only if the triangle is isosceles.

    Thanks for your help.
    Draw a parallel line from the vertex to the given side.
    Taking any point on this lin, if you draw a triangle with the given side, all the triangles will have the same area.
    If a and b are the sides of the triangles,and b> a then angle B>A.
    According to sine rule
    a/sinA = b/sinB.
    So a = k*sinA
    b = k*sinB.
    Hence a + b = k(sinA + sinB) > 2*k*sinA
    So a+b will be minimum if a = b.
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