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    Let a and b be positive real numbers. And x^2 + y^2 is less than or equal to 1 . You have to find the maximum value of ax+by.

    This image was included as part of the solution. What I don't understand is why the diagonal length labelled is a/b.
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    (Original post by stolenuniverse)
    Let a and b be positive real numbers. And x^2 + y^2 is less than or equal to 1 . You have to find the maximum value of ax+by.

    This image was included as part of the solution. What I don't understand is why the diagonal length labelled is a/b.
    The solution does seem rather opaque in its reasoning. Perhaps the easiest way to appreciate why that lenght is a/b is to appreciate it as the tangenet of certain angles.

    PS Especially as at a second glance it's clear the equation of the line has been incorrectly rearranged.
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    (Original post by stolenuniverse)
    Let a and b be positive real numbers. And x^2 + y^2 is less than or equal to 1 . You have to find the maximum value of ax+by.

    This image was included as part of the solution. What I don't understand is why the diagonal length labelled is a/b.
    The small triangle with side 1 is similar to the big triangle made with the line ax+by=c as the hypotenuse. The big triangle has vertical/horizontal sides ka and kb for some k (since the gradient is a/b), so the ratio of those sides is a/b which must also be the ratio of the corresponding sides in the smaller triangle.
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    (Original post by RichE)
    The solution does seem rather opaque in its reasoning. Perhaps the easiest way to appreciate why that lenght is a/b is to appreciate it as the tangenet of certain angles.

    PS Especially as at a second glance it's clear the equation of the line has been incorrectly rearranged.
    Has it? Those lengths look OK to me.
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    (Original post by atsruser)
    Has it? Those lengths look OK to me.
    The lengths are fine. Go to the full MAT solution to see the error of rearrangement.
 
 
 
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