 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Three Altitudes (Posted on 2007-01-15) If the lengths of the altitudes of a triangle are 4, 5, and 6, what is the area of the triangle?

Can you generalize?

 Submitted by Dennis Rating: 3.0000 (1 votes) Solution: (Hide) If h, j, and k represent the lengths of the altitudes of a triangle, the area of the triangle is given by the equation: A=(hjk)^2/sqrt(2(hjk)^2(h^2+j^2+k^2)-((hj)^4+(hk)^4+(jk)^4)) The above formula is derived by solving simultaneously the six pythagorean equations involving the altitudes and the segments of the sides they partition. Letting h=4, j=5, and k=6 --> A=3600/sqrt(57239) --> the sides have lengths 1200/sqrt(57239), 1440/sqrt(57239), and 1800/sqrt(57239). Comments: ( You must be logged in to post comments.)
 Subject Author Date No Subject Amanda 2007-01-16 00:26:27 researched solution Charlie 2007-01-15 23:21:07 Solution Bractals 2007-01-15 17:43:05 Please log in:
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