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

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! ðŸ˜›

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! ðŸ˜›

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 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! ðŸ˜›

Erm...you have two triangles, one having sides of length 2, 3, x, and the other 3, 4, x. (X is side of square.) Finding the areas of each triangle and noting y^+z^2 = 9 (where y and z are the heights of these triangles) gives:

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

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

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

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.

I hope you use your Math for all that is good and right!

Yes, 8 locations it is. If you care, check it out.