Question 243200: A triangle has sides with lengths in centimeters that are consecutive even integers. Find the
lengths if the perimeter is 186 cm.
Found 2 solutions by checkley77, oberobic:
Answer by checkley77(12844)   (Show Source):
You can put this solution on YOUR website! Let x, x+2 & x=4 be the 3 even integers.
x+x+2+x+4=186
3x=186-2-4
3x=180
x=180/3
x=60 cm. for the shortest side.
60+2=62 cm. for the middle side.
60+4=64 cm. for the longest side.
Proof:
60+62+64-186
186=186
Answer by oberobic(2304) (Show Source):
You can put this solution on YOUR website! 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.
...
Substituting for the 3 sides in the perimeter equation, we have:
x + x+2 + x+4 = 186
...
Collecting like terms, we have:
3x + 6 = 186
...
Subtracting 6 from both sides:
3x = 180
...
Dividing both sides by 3:
x = 60
So, a = 60.
...
x + 2 = 60 + 2 = 62
So, b = 62
...
x + 4 = 60 + 4 = 64
So, c = 64
...
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.
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