Find the dimensions and orientation of the largest area (a) square and (b) rectangle you can draw inside an equilateral triangle of side 1
(In reply to
disagree by xdog)
xdog,
By inspection, I agree.
If the side of the equilateral triangle is 1, the square has area (2112*(3)^(1/2)) and (2112*(3)^(1/2))^(1/2) = 2*3^(1/2)3; the ratio of the triangle to the square is then 1+7/(4*3^(1/2)) to 1
Similarly, the rectangle has area 3^(1/2)/8 and the ratio of the triangle to the rectangle is 2 to 1.

Posted by broll
on 20131202 07:25:39 