SOLUTION: A wooden fence surrounds a garden that is in the shape of an irregular triangle. If one side is twice as long as the first, and another is half as long as the first side, and the f

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Question 149757: A wooden fence surrounds a garden that is in the shape of an irregular triangle. If one side is twice as long as the first, and another is half as long as the first side, and the fence is 70 feet long, what are the dimensions of the garden?
( Make a drawing, assign a variable, answer the question asked, check your work)
Thank you very much.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=length of first side.


Since "one side is twice as long as the first", this means that y=2x


Also, because "another is half as long as the first side", this means that z=%281%2F2%29x



However, there's a problem. In order for any triangle to be constructed, the lengths of any two sides must be greater than the length of the third side. So for instance, this means that x%2Bz%3Ey.

x%2B%281%2F2%29x%3E2x Plug in y=2x and z=%281%2F2%29x


%283%2F2%29x%3E2x Add


Since this inequality is never true for any positive x values, this means that you cannot construct a triangle with sides of x, 2x, and %281%2F2%29x (go ahead and try it out on paper if you don't believe me).


So I would double check the problem.