Question

ageagheah

Answer 1

First, we need the vectors,
\[\vec{AB} =B-A=(-1,2,2)-(2,4,1)=(-3,-2,1)\]\[\vec{AC} =C-A=(7,0,4)-(2,4,1)=(5,-4,3)\]\[\vec{CB} =B-C=(-1,2,2)-(7,0,4)=(-8,2,-2)\]
Then, we find the modulus of each vector,
\[|\vec{AB}|=\sqrt{3^2+2^2+1}=\sqrt{14}\]\[|\vec{AC}|=\sqrt{5^2+4^2+3^2}=\sqrt{50}\]\[|\vec{CB}|=\sqrt{8^2+2^2+2^2}=\sqrt{72}\]
Then, the perimeter is,
\[P=\sqrt{14}+\sqrt{50}+\sqrt{72}\]

Answer 2

unfortunately, that's definitely not what it is. :(

Answer 3

Do you have the answer?, please write to compare ;)

Answer 4

Are you sure about that? That's what WolframAlpha reports for the perimeter of a triangle with those vertices...

Answer 5

Is the answer expected in symbolic or numeric form?

Answer 6

\[\sqrt{14}+\sqrt{50}+\sqrt{72} = \sqrt{14} + \sqrt{2*25}+\sqrt{2*36}\]\[ = \sqrt{14}+5\sqrt{2} + 6\sqrt{2} = 11\sqrt{2}+\sqrt{14}\]

Answer 7

Exact

Answer 8

That's as exact as it gets.

Answer 9

numeric. its one of : 27.2, 22.1, 15.1, 18.1

Answer 10

Maybe he needs the approximate result, 19.298

Answer 11

Are you sure you have all of the coordinates correctly stated above?

Answer 12

yes.

Answer 13

Please, could you rewrite the coordinates again?

Answer 14

Well, see perimeter value given here: http://www.wolframalpha.com/input/?i=triangle++%282%2C4%2C1%29%2C+%28-1%2C2%2C2%29+%2C%287%2C0%2C4%29

Answer 15

Yes, in the link from above, you will see that the result is correct. So the coordinates must be others if the results are what you write.

Answer 16

If c(7,0,-4) instead of c(7,0,4) the result is 22.06 which matches 22.1 after rounding...

Answer 17

than kyou

Answer 18

is that the error?