Given an equilateral triangle inscribed in a circle with a radius R.
Evaluate the dimensions (height, width) of an inscribed rectangle with the same area as the triangle.
WLOG, let R=1/3^(1/2)
Then a side of the equilateral triangle has length 1
The rectangle then has
height 0.3997121328165.., close to 1/2 sqrt(1/3(8sqrt(37))), and
width 1.0833113791577.., close to 1/2 sqrt(1/3(8+sqrt(37))),
just a little less than a diameter = 2R=1.154700538379...
Edited on March 16, 2016, 6:27 am

Posted by broll
on 20160316 05:22:07 