Question 243200
Always start with the facts and mathematical properties you know.
Perimeter of a triangle = sum of sides = a + b + c = 186 (given).
The lengths of the sides are consecutive EVEN integers: x, y, z.
But that creates a problem with too many unknowns.
However, there is a better way to depict three consecutive even integers:
a = x
b = x + 2
c = x + 4
Then when we solve the equation we can determine if x is even.  If not, there's no solution.
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Substituting for the 3 sides in the perimeter equation, we have:
x + x+2 + x+4 = 186
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Collecting like terms, we have:
3x + 6 = 186
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Subtracting 6 from both sides:
3x = 180
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Dividing both sides by 3:
x = 60
So, a = 60.
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x + 2 = 60 + 2 = 62
So, b = 62
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x + 4 = 60 + 4 = 64
So, c = 64
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Our proposition is that the 3 sides that are consecutive integers are: 60, 62 & 64.
We can check by substituting back into the givens.
Do 60 + 62 + 64 qualify as consecutive even integers. Yes.
Does 60 + 62 + 64 = 186?  Yes.
Done.