Consider trapezoid ABCD where BC is perpendicular to AB and CD. Consider also that the diagonals AC and BD are perpendicular to each other and intersect at point E.
If EA = 6.25 and ED = 3.2, then what are EB and EC?
Triangles AEB, BEC, and CED are similar. Therefore,
|EA| |EB| |EC|
------ = ------ = ------
|EB| |EC| |ED|
Thus,
|EB| = |EC| = |ED| = |EA|
or
|EB| = (|ED||EA|^2)^(1/3) and |EC| = (|ED|^2|EA|)^(1/3)
For our problem |ED| != |EA|. Therefore,
|EB| = ((3.2)(6.25)^2)^(1/3) = 5
|EC| = ((3.2)^2(6.25))^(1/3) = 4
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Posted by Bractals
on 2007-03-03 14:54:28 |
Solution
