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# MAT question, help? watch

1. 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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2. (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.
3. (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.
4. (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.
5. (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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