I am not sure on how to start this problem. I just need a little help in starting the problem and I am certain that I can solve it, but I'm stumped on how to start. Any suggestions?
Find the dimensions of the rectangle that will maximize its area if it is inscribed into a triangle.
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3How have you used the hint they gave? That's how you start. – Ted Shifrin Dec 15 '19 at 19:02
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Find out how $x$ and $y$ are related. – peterwhy Dec 15 '19 at 19:02
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The thing is that I don't know how the hint helps me in this case. I know that the area of the rectangle is x * y, but how do I find out how they are related? – P1081 Dec 15 '19 at 19:14
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1Does this answer your question? Maximizing the area of rectangle inscribed in triangle – amd Dec 15 '19 at 19:14
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1That problem involves using coordinates to answer the question. I don't think that could help me with this problem. I just don't get how the hint helps me find more information. – P1081 Dec 15 '19 at 19:19
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Fix $A$ to $(0,0)$. Then we have $E(20,0)$ and $C(t,12)$. – Andrew Chin Dec 16 '19 at 09:15
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Using the hint, we know that $x/20=(12-y)/12$ (Because the triangles are similar) $\Leftrightarrow$ $x=20-(5/3) y$
We want the maximum value Area, which is ${x}{y}\ $, or $20y-(5/3)y^2$, so we differentiate and equal to $0$.
$\frac{d}{dy}(20y-(5/3)y^2)=0 \Leftrightarrow y = 6\ $. Plugging it in the previous formula we get that the maximum value of the area is $60$ and the minimum is obviously $0$.
RicardoMM
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