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bazinga276 Group Title

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)

  • one year ago
  • one year ago

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  1. satellite73 Group Title
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    put the side of the triangle as \(x\) and the side of the square is \(y\) then \[3x+4y=10\] solve for \(y\) get \[y=\frac{10-3x}{4}\]

    • one year ago
  2. satellite73 Group Title
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    total area is therefore what you said triangle area is \(A(x)=\frac{\sqrt{3}x^2}{4}+(\frac{10-3x}{4})^2\)

    • one year ago
  3. bazinga276 Group Title
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    After taking the derivative of that, I get \[A'=\frac{ 4\sqrt{3}x+9x-30 }{ 8 }\] Am I on the right path?

    • one year ago
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