SOLUTION: The perimeter of a triangle is 83 inches. The longest side is three times the length of the shortest side and 17 inches more than one-half the sum of the other two sides. Use a s

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Question 158796This question is from textbook Advanced Mathematical Concepts
: The perimeter of a triangle is 83 inches. The longest side is three times the length of the shortest side and 17 inches more than one-half the sum of the other two sides. Use a system of equations to find the length of each side. I don't really understand this and I asked some people to help, but they couldn't get it either. Please help me... Thanks! This question is from textbook Advanced Mathematical Concepts

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
Longest side=3*shortest side.
Longest side=17+(shortest side + other side)/2
3ss=17+(ss+os)/2
os/2=3ss-17-ss/2
0s/2=2.5ss-17
os=5ss-34
3ss+ss+5ss-34=83
9ss=83+34
9ss=117
ss=117/9
ss=13 inches for the short side.
ls=3*13=39 inches for the long side.
os=5*13-34=31 inches for the other side.
Proof
13+39+31=83
83=83