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Tidy Triangle (Posted on 2006-05-05)

Find the smallest obtuse triangle such that its sides, the altitude to the obtuse angle, and the median to the largest side are all integers.

In case it arises, "smallest" refers to the area of the triangle.

Submitted by Jer

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Solution: (Hide)

The absolute smallest fitting the conditions is a triangle with sides 5, 5, and 6. Its altitude and median are both the same line of length 4.
If the altitude and median must be different the smallest is a triangle with sides 25, 39, and 56. Its altitude is 15 and its median is 17.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Oops!	Richard	2006-05-19 13:40:44
re(3): If not different	Richard	2006-05-06 15:35:58
re(2): If not different	Dej Mar	2006-05-06 06:13:02
re(2): If not different	Richard	2006-05-05 22:18:19
re: If not different	Eric	2006-05-05 22:09:00
If not different	Gamer	2006-05-05 20:00:50
computer trial-and-error solution (spoiler)	Charlie	2006-05-05 15:32:40

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