 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Equilateral Triangle 123 (Posted on 2007-09-05) An equilateral triangle lies with its three vertices at respective distances from the origin as 1, 2 and 3 units. What is the length of each side of the triangle?

 See The Solution Submitted by Charlie Rating: 4.0000 (3 votes) Comments: ( Back to comment list | You must be logged in to post comments.) Solution | Comment 2 of 3 | `Let (x_1,y_1), (x_2,y_2), and (x_3,y_3) be thevertices of the equilateral triangle and s itsside length. WOLOG let (x_1,y_1) = (1,0). Then`
`  x_2^2 + y_2^2 = 4                       (1)`
`  x_3^2 + y_3^2 = 9                       (2)`
`  s^2 = (x_2 - 1)^2 + y_2^2               (3)`
`  s^2 = (x_3 - 1)^2 + y_3^2               (4)`
`  s^2 = (x_3 - x_2)^2 + (y_3 - y_2)^2     (5)`
`Combining equations 1 and 3 gives`
`  s^2 = 5 - 2*x_2                         (6)`
`Combining equations 2 and 4 gives`
`  s^2 = 10 - 2*x_3                        (7)`
`Combining equations 6 and 7 gives`
`  x_3 = x_2 + 5/2                         (8)`
`Combining equations 1, 2, 5, 6, and 8 gives`
`  (x_2 + 1)^2*(2*x_2 - 5) = 0             (9)`
`The value x_2 = 5/2 does not satisfyequation (1). Therefore,`
`  x_2 = -1`
`     and`
`  s = sqrt(7)`
` `

 Posted by Bractals on 2007-09-05 10:43:23 Please log in:

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