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anonymous

  • 5 years ago

Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral triangle of side L=2 cm if one side of the rectangle lies on the base of the triangle.

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  1. dumbcow
    • 5 years ago
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    max Area = sqrt(3)/2

  2. anonymous
    • 5 years ago
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    On the side of the triangle shared with a side of the rectangle call x the distance from one corner of the triangle to the start of the base of the rectangle. Then the height of the rectangle is x*tan(60)=x*sqrt(3). So the area is (2-2x)*(x*sqrt(3))=2xsqrt(3)-2x^2sqrt(3). We take the derivative and set equal to 0. 2sqrt(3)-4sqrt(3)x=0 x=1/2 So the base is 1 and the height is sqrt(3)/2 Max area =sqrt(3)/2

  3. anonymous
    • 5 years ago
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    Thank you both very much!

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