The Well in the Field

In a square field, there is a well. The distance between the well and the northeast corner is 30 metres. The distance between the well and the southeast corner is 50 metres, and the distance between the well and the southwest corner is 70 metres. What is the area of the field?

This puzzle is rather more difficult than it appears at first. It is possible to solve, though. You will likely need to use trigonometry to solve it. It's not super-hard, though. I managed to solve it in about ½ of a page of calculations. The solution doesn't require using any concepts not taught in high school either.

I have not provided a solution online to encourage people to try the problem first. The solution can, however, be found in my e-book, Solving Math Problems. If you have questions about the problem or the solution, please e-mail mathlair@allfunandgames.ca.

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