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Ellipses (Posted on 2004-05-17) Difficulty: 5 of 5
What is the area of the smallest ellipse that can be circumscribed around a 3-4-5 triangle?

What is the area of the largest ellipse that can be inscribed in a 3-4-5 triangle?

No Solution Yet Submitted by SilverKnight    
Rating: 3.8333 (6 votes)

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Hints/Tips Part 1 | Comment 2 of 12 |
Since the triangle is 3-4-5. this makes it a right angle triangle.

The hypotenuse of this triangle must be the major axis of the ellipse with the right angle portion of the triangle sitting on the edge of the ellipse.
If the above is true then the ellipse is actually a circle. with the diameter equal to the hypotenuse of the triangle.

Therefore the smallest "ellipse" that can be circumscribed is

2.5 x 2.5 x 3.14159 = 19.635.

  Posted by Juggler on 2004-05-17 23:29:38
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