Buried Treasure

A treasure is buried in a square field such that it is 2 miles from one corner, 3 from the next, and four from the next corner. What is the area of the field?

Originally posted by royalchicken
A treasure is buried in a square field such that it is 2 miles from one corner, 3 from the next, and four from the next corner. What is the area of the field?

Originally posted by UncleAdam
6 miles by 6 miles?

Originally posted by royalchicken
No....not 6x6...how did you solve it...possibly you have just made a small error.

Originally posted by UncleAdam
it looks something like this right?

- - 3 - - -
- - - - - -
- - - - - -
- - - - - -
2 - T - - 4
- - - - - -

with the T for the
treasure and the - for a mile and a # for where the # would come from to get there

Originally posted by royalchicken
Distances from corners. Measured on diagonals. 4 > 3.

18 sq. miles

25

Originally posted by bbarr
18 sq. miles

Originally posted by royalchicken
Very good, bbarr. 10+3*sqrt(7) =~ 17.9

Originally posted by Phlabibit
2 tangent circles of 2 miles and 4 miles intersect about 3.162 miles from either remaining corners. Area of said square is 17.9999. Math never works! 😛

Originally posted by waldorf
Nice try

Originally posted by Phlabibit
Good luck finding that treasure because that gives you 4 possible locations in a field to dig with an area of a 1/4 mile each. I'll take the map please!

Originally posted by Phlabibit
2 tangent circles of 2 miles and 4 miles intersect about 3.162 miles from either remaining corners. Area of said square is 17.9999. Math never works! 😛

Originally posted by royalchicken
Erm...you have two triangles, one having sides of length 2, 3, x, and the other 3, 4, x. (X is side of square.) blah blah blah.... gives:

x^4 - 20x^2 + 37 =0

or x^2 = 10 + 3*Sqrt(7).

There are 8 possible places, four corners, two directions.