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Posted 28 February 2008 - 11:09 PM
But it occurred to me it's easy to show the sum of squared distances to diagonally opposite corners are the same.
Let horizontal and vertical lines through the cow divide the fences into lengths u and v vertically and w and x horizontally.
Squared distance to one corner is u2 + x2 and to the diagonally opposite corner, v2 + w2.
Squared distances to the other two corners are u2 + w2 and v2 + x2.
The squared distances in both cases add to u2 + x2 + w2 + v2.
Vidi vici veni.
Posted 28 February 2008 - 11:35 PM
I have got a square field with one cow. My cow lied 13 meters from one of the corner posts of the field, 17 meters from the corner post diagonally opposite that one, and 20 meters from a third corner post. Can someone tell me how big (perimeter) a field I own?
You may assume the field is flat, and the distance of the cow from the corner poles is measured from the center of mass of the cow -- you know what I mean.
Posted 29 February 2008 - 09:48 PM
Redo of my answer:
the OP said it was a square field. Meaning the 30m diagonal cuts it into two right triangles, with the hypotenuse of 30 m, so each side of both right triangles (in other words, one side of the 4 equal sides of the square), would be 15*sqrt(2) meters. Multiply by 4 to get 60*sqrt(2), which is approx 84.853 meters perimeter
Posted 29 February 2008 - 09:49 PM
Posted 01 March 2008 - 06:09 PM
Oh I see, nevermind- he doesnt have to be necessarily on the diagonal between the corners. Woops! lol
Ya, the cow may not be on the diagonal. There are good diagrams on posts #12, 15 and 20. IMHO, they will be very helpful.
Edited by brhan, 01 March 2008 - 06:10 PM.
Posted 01 March 2008 - 08:54 PM
Posted 01 March 2008 - 09:29 PM
Hold on... There's two fields. And the cow is loose!
Waw, that is great Bonanova ... exploring for the second solution. Interesting explanation.
Posted 01 March 2008 - 09:30 PM
Yeah I was just like "17m from one corner, 13m from the other, means the diagonal is 30m, wow this is an easy problem!" before I actually thought enough to see that it didn't have to be right on the diagonal hehe. I'd rather not look at the pictures or the answers, I'll figure it out myself ;D (if i can, that is. hehe)
Alright, that is great. I am sure will solve it.
Posted 02 March 2008 - 12:58 AM
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