Question 110541: I am given that there is a equiangular triangle ABC. Side AB is 17 units, side BC is 5x-y and side AC is 7x+2y. I need to write my answer in standard form of Ax+By=C but do not have to solve.
I just dont understand how to do this when x & y are together. Thanks.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! One of the things that will help you here is to recognize that an equiangular triangle
(all three angles are equal and therefore are 180/3 = 60 degrees) is also an equilateral
triangle (all sides equal).
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Since you are told that side AB is 17 units, you know then that side BC and side AC are each
17 units long also.
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You are told that side BC is 5x - y and you know that it is also 17 units long. Therefore,
for side BC you can write:
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5x - y = 17
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Next you are told that side AC is 7x + 2y and you know that it is also is 17 units long.
Therefore, for side AC you can write:
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7x + 2y = 17
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So for this triangle you now have two equations:
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5x - y = 17 <==== for side BC ... and
7x + 2y = 17 <=== for side AC
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These are the two equations you are looking for. Since you have two linear equations
with two unknowns, assuming that they are independent, you could solve for x and y.
In case you try it, the answers are x = 3 and y = -2. If you substitute these two values
into the left side of the equations for BC and AC you should find that the left sides of
these two equations actually does equal 17.
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Hope this helps you to understand the problem a little better.
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