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This is my first post on here, I was hoping it wouldn't be asking for help but I don't have any options left and it's a problem that is due soon. I promise I have tried to solve it myself but I'm unsure if I'm doing it correctly and it is part of a take home test.

1. The problem statement, all variables and given/known data

The question is:

You are planning to close off a corner of the first quadrant with a line segment 19 units long running from (x,0) to (0,y). Show that the area of the triangle enclosed by the segment is largest when x=y.

2. Relevant equations

I have A=1/2bh (area = 1/2 base * height) and I know that is what I have to take the derivative of and I know I have to set that equal to zero and solve for it.

What I'm not sure is if I can consider this a right triangle. It says the "a corner of the first quadrant" so I'm assuming that this is the first quadrant of the Cartesian graph and that it is indeed a right angle.

3. The attempt at a solution

I've tried using the Pythagorean theorem, solving for one of the legs (e.i. b = (19^2 - h^2)^1/2 [ b = base and h= height]) and I put that into the area equation, simplify, and take the derivative of it.

I think I keep screwing the derivative up while doing that. I'm also not sure if I can even be using the Pythagorean theorem.

I've asked other people in my class, I've checked three textbooks looking for similar examples, I've search for videos like it, search the web and I can't find anything like this to help me.

Any help would be greatly appreciated.

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# Homework Help: Optimization of a Triangles Area.

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