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## The Oil Problem

Posted by ragknot on December 13, 2012 – 11:30 pm

An oil well being drilled in flat prairie country struck pay
sand at an under ground spot exactly 21,000 feet from one corner of a rectangular plot of farmland, 18,000 feet from the opposite corner, and 6000 feet from a third corner.

How far is the underground spot from the fourth corner ?

This post is under “Tom” and has 8 respond so far.

### 8 Responds so far- Add one»

1. 1. DP Said：

There are two answers I can find to this problem.
If by opposite you mean diagonally opposite, then the answer is 27,000 feet.
If by opposite you mean share a common side of the rectangle, then the answer is 12,369. The only way for this to happen is if the 21,000 and 18,000 corners share a side of the rectangle, and so do the 18,000 and 6,000 dimensions. It is not possible for the 21,000 and 6,000 dimensions to share a side and the point be 18,000 feet from another corner.
I suspect you were looking for the 27,000 feet.

2. 2. Chris Said：
```
o   a    o           c           o
d                                d
o        X                       o

b                                b

o   a    o           c           o
```

Let the origin be at the bottom left corner of the rectangle, i.e. (0, 0)
Let the spot be at (a, b).
Let the top left corner be at (0, b+d).
Let the bottom right corner be at (a+c, 0)
Then the top right corner is at (a+c, b+d)

I’ll use units of 1000 feet. We have:

{E1} a² + b² = 18²
{E2} c² + d² = 21²
{E3} a² + d² = 6²

We want to find x, such that x² = b² + c²

{E1} + {E2} => (a² + b²) + (c² + d²) = 18² + 21²
= (b² + c²) + (a² + d²) = x² + 6²
=> x² = 18² + 21² – 6² = 729 = 27²
So x = 27 (thousand) feet

If I’d used the bottom right corner, rather than the top left corner, as being
the one that was 6 (thousand) feet from the spot, I get the same result

3. 3. ragknot Said：

Correct 27000

This was added to ToM many years ago. But I don’t know who did it right, then.

4. 4. abhay Said：

1.27000
2.13000

5. 5. Dusty Said：

Well according to the people above I’ve done something wrong in my math, but, I believe the correct answer to be 28,301.943 ft. Quite a brain twister! THANKS!!

6. 6. Chris Said：

I had assumed that the spot was inside the rectangle. If it is outside, you still get 27,000 feet for the last distance.

7. 7. DI Said：

Simple logic states that if it is any distance from 3 corners and it is a rectangle, Then the spot itself would be the 4th corner.

8. 8. Chris Said：

Hi DI. No it doesn’t. See my post (2) for how to do it.

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