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A Square, a Rectangle and a Triangle (Posted on 2013-11-17) Difficulty: 3 of 5
Find the dimensions and orientation of the largest area (a) square and (b) rectangle you can draw inside an equilateral triangle of side 1

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 3.0000 (1 votes)

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re: disagree Comment 3 of 3 |
(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
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