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Same area (Posted on 2016-03-15) Difficulty: 3 of 5
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.

See The Solution Submitted by Ady TZIDON    
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Some Thoughts Possible solution | Comment 1 of 2

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(8-sqrt(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 2016-03-16 05:22:07

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