Question 201630: In a triagle,the second side is one-third of the first side in length. The third side is 2 meters less than the first side. The perimeter of the triangle is 26 meters. Form an algebraic equation to express this problem.
Found 3 solutions by jim_thompson5910, checkley77, MathTherapy:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Let
x = length of the first side,
y = length of the second side, and
z = length of the third side
Since "the second side is one-third of the first side in length", this means that  . Also, because "The third side is 2 meters less than the first side", we know that 
Recall that the perimeter "P" of ANY triangle with sides of "x", "y", and "z" is 
Start with the given equation.
 Plug in  (the given perimeter), , and
So the algebraic equation is
If you wanted to find the lengths of the three sides, you would then solve for "x" (to eventually find "y" and "z"). Since the problem doesn't ask for it, I'll stop here. Let me know if you want to keep going.
Answer by checkley77(12844) (Show Source):
You can put this solution on YOUR website! x+x/3+x-2=27
(3x+x+3x-2*3)/3=27
7x-6=3*27
7x=6+81
7x=87
x=87/7 ans.
Proof:
87/7+(87/7)/3+87/7-2=27
87/7+87/7*1/3+87/7-2=27
87/7+87/21+87/7-14/7=27
(3*87+87+87*3-14*3)/21=27
(261+87+261-42)/21=27
567/21=27
567=21*27
567=567
Answer by MathTherapy(10809)  (Show Source):
You can put this solution on YOUR website!
Let the second side be s
Since the first side is 3 times the second (same as 2nd side being 1/3 of the first), then first side is 3s
And, since the third side is 2 meters less than the first side, then its length is 3s – 2
Together, their sum is 26. Therefore, the algebraic equation to express this situation is: 
Going further, and solving this equation, we can see that the second side, or s, is 4 meters, the first side, or 3s, is 12 (3*4) meters, and the third side, or 3s - 2, is 10 (3*4-2) meters. Altogether, they add up to 26 (4 + 12 + 10) meters, the perimeter of the triangle.
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