Question

cattle feeders a cattle rancher wants to place three feeders in his pasture. he researches feeder locations and determines that the most efficient layout is for the feeders to be placed an equal distance from each other and one hundred feet apart. with this information, would he be able to locate all three feeders along a straight fence line?

Explanation:

If three points are on a straight line, the distance between the two outer - most points is the sum of the distances between adjacent points. If three feeders are on a straight line and the distance between each adjacent pair is \(d = 100\) feet, then the distance between the first and the third feeder is \(D=100 + 100=200\) feet. But if three points are equidistant from each other (in a non - collinear case, they form an equilateral triangle where all side lengths are equal). However, the problem asks if they can be placed along a straight fence line. If we assume the three feeders \(A\), \(B\), and \(C\) are on a straight line. Let \(AB = 100\) and \(BC = 100\). Then \(AC=AB + BC=200
eq100\). So, it is not possible.

Answer:

No, it is not possible.