Maxima problem

Consider all of the triangles formed by lines passing through the point (8/9,3) and both the x and y axes. Find the dimensions of the triangle with the longest hypotenuse.

Not looking for an answer, but just a nudge in the right direction. I know I have to find two equations, solve for one variable, and differentiate. The problem is, other than a^2+b^2=C^2, I can't seem to think of anything else that would help.

I have a ton of these, and they're all different, so expect a few more questions from me. thanks for all the help - I'm jealous of all this comes easy to.

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Originally Posted by BooGTS

Consider all of the triangles formed by lines passing through the point (8/9,3) and both the x and y axes. Find the dimensions of the triangle with the longest hypotenuse.

Not looking for an answer, but just a nudge in the right direction. I know I have to find two equations, solve for one variable, and differentiate. The problem is, other than a^2+b^2=C^2, I can't seem to think of anything else that would help.

I have a ton of these, and they're all different, so expect a few more questions from me. thanks for all the help - I'm jealous of all this comes easy to.

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This seems impossible...

As stated, there are only two lines that don't meet the criteria. One horizontal, the other vertical. Now, you can imagine that if you were to tilt this line just a wee bit, it would pass through the x and y axes, but the hypotenuse relative to the origin would be extremely long. And if we tilted a bit less, longer still, ad in finitum. So, are you sure that we aren't looking for the line with the SHORTEST hypotenuse?

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Originally Posted by VonNemo19

This seems impossible...

As stated, there are only two lines that don't meet the criteria. One horizontal, the other vertical. Now, you can imagine that if you were to tilt this line just a wee bit, it would pass through the x and y axes, but the hypotenuse relative to the origin would be extremely long. And if we tilted a bit less, longer still, ad in finitum. So, are you sure that we aren't looking for the line with the SHORTEST hypotenuse?

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I'll ask for a hint from the prof if she responds, but yeah, I copied it right. We're getting the answer tomorrow, and I'll post it here, but I have no idea at the moment. Don't suppose you live close to Rochester? (ha)

Quote:

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Originally Posted by BooGTS

I'll ask for a hint from the prof if she responds, but yeah, I copied it right. We're getting the answer tomorrow, and I'll post it here, but I have no idea at the moment. Don't suppose you live close to Rochester? (ha)

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I do live close to rochester. 10 minutes maybe.

I've thought more about your problem, and it's nonsensical...