Find the dimensions and orientation of the largest area (a) square and (b) rectangle you can draw inside an equilateral triangle of side 1
I took rectangle to mean non-square.
Square
A square side=x aligned with one side on the base of the triangle and the other corners touching the other sides gives a 30-60-90 triangle with the vertical side=sqrt(3)*(1-x)/2. But this side=x and x = sqrt(3)/(2 + sqrt(3)) = 2*sqrt(3) - 3 and area = .2153903091+
Rectangle.
x=width, y=heighth. Using the same 30-60-90 triangle, y = sqrt(3)*(1-x)/2 and area xy = x*sqrt(3)*(1-x)/2 which is minimum when x = 1/2, so y=sqrt(3)/4, area = sqrt(3)/8 = .2165063509+
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Posted by xdog
on 2013-11-18 19:33:32 |
disagree
