SOLUTION: Please help me solve this problem: A triangle has a perimeter of 197 centimeters. The sum of the smallest and middle side is 49 more than the longest side. The difference of the

Question 181970: Please help me solve this problem:
A triangle has a perimeter of 197 centimeters. The sum of the smallest and middle side is 49 more than the longest side. The difference of the longest and shortest side is 22. Find the lengths of the three sides of the triangle.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A triangle has a perimeter of 197 centimeters. The sum of the smallest and middle side is 49 more than the longest side. The difference of the longest and shortest side is 22. Find the lengths of the three sides of the triangle.
:
Three sides, a, b, c (c is the longest)
:
write an equation for each statement
:
"A triangle has a perimeter of 197 centimeters."
a + b + c = 197
:
"The sum of the smallest and middle side is 49 more than the longest side."
a + b = c + 49
a + b - c = 49
:
"The difference of the longest and shortest side is 22."
c - a = 22
:
Find the lengths of the three sides of the triangle.
:
Use elimination on the the 1st and 2nd equation
a + b + c = 197
a + b - c = 49
------------------subtraction eliminate a & b, find c:
2c = 148
c =
c = 74
:
then
c - a = 22
74 - a = 22
-a = 22 - 74
-a = -52
a = 52
:
a + b + c = 197
52 + b + 74 = 197
b + 126 = 197
b = 197 - 126
b = 71
:
a=52, b=71, c=74
:
Check solution in the equation: a + b = c + 49
52 + 71 = 74 + 49
123 = 123
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