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bazinga276
 3 years ago
The sum of the perimeters of an equilateral triangle and a square is 10. Find the dimensions of the triangle and square that produce a minimum area.
I would like to solve it by incorporating A=(sqrt(3)x^2)/4 (area of an equilateral triangle)
bazinga276
 3 years ago
The sum of the perimeters of an equilateral triangle and a square is 10. Find the dimensions of the triangle and square that produce a minimum area. I would like to solve it by incorporating A=(sqrt(3)x^2)/4 (area of an equilateral triangle)

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satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1put the side of the triangle as \(x\) and the side of the square is \(y\) then \[3x+4y=10\] solve for \(y\) get \[y=\frac{103x}{4}\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1total area is therefore what you said triangle area is \(A(x)=\frac{\sqrt{3}x^2}{4}+(\frac{103x}{4})^2\)

bazinga276
 3 years ago
Best ResponseYou've already chosen the best response.0After taking the derivative of that, I get \[A'=\frac{ 4\sqrt{3}x+9x30 }{ 8 }\] Am I on the right path?
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