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 A Point and a Cube (Posted on 2004-07-16)
Before tackling this one, take a look at this one.
```     +-------------D
/|            /|
/ |           / |
/  |          /  |
/   |         /   |
C-------------+    |
|    |        |    |
|    B--------|----+
|   /         |   /
|  /          |  /
| /           | /
|/            |/
+-------------A
```
A, B, C and D are non-adjacent vertices of a cube. There is a point P in space such that PA=3, PB=5, PC=7, and PD=6. Find the distance from P to the other four vertices and find the length of the edge of the cube.
There are two answers, one with P outside the cube and one with P inside the cube.

 No Solution Yet Submitted by Brian Smith Rating: 4.0000 (5 votes)

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 Algebraic solution Comment 23 of 23 |

My solutions for the length of side/edge are:

Sqrt[(119 - 4*Sqrt[238])/6],

Sqrt[119/6 + (2*Sqrt[238])/3]

obtained by solving for positive real s:

x^2 + y^2 + z^2 = 9,

(s - x)^2 + (s - y)^2 + z^2 = 25,

x^2 + (s - y)^2 + (s - z)^2 = 49,

(s - x)^2 + y^2 + (s - z)^2 = 36

 Posted by goFish on 2006-02-24 06:12:23

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