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## Question

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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.

Edited by brhan

## 35 answers to this question

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Guest
Hold on... There's two fields. And the cow is loose!

Waw, that is great Bonanova ... exploring for the second solution. Interesting explanation.

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Guest
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.

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Working on it now

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I got extremely frustrated trying to solve this problem, lol. I looked at the various answers, and none of them make any sense. Can anyone explain the solution in very very very simple words, please?

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Well I did figure out this:

(attached)

But I dont know if that helps

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Guest

there would be 10 meters to the non-mentioned post- seeing that its a square- its legnth times width for area right- so 30 x 30 would be 1800 km sq

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Guest

not km just meters.

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Guest

i think im wrong now.....

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bonanova    76
Well I did figure out this:

[diagram and equations]

But I dont know if that helps

... plug in b=13 c=17 and d=20, solve for the s's, add them and double it.

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ah thanks, bonanova

b^2 + c^2 = s1^2 + s2^2 + s3^2 + s4^2

458 = s1^2 + s2^2 + s3^2 + s4^2

so now what? How do you solve for the s's? There could be a zillion answers, right? Or do you somehow use s1+s2=s3+s4 to help narrow it down? I'm still confused ;D

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