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 (21-12*(3)^(1/2)) and (21-12*(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 2013-12-02 07:25:39