SOLUTION: The perimeter of a triangle is 110cm. one side is twice the second side. the third side is 30cm more than the second side. find the length of each side

Question 243639: The perimeter of a triangle is 110cm. one side is twice the second side. the third side is 30cm more than the second side. find the length of each side
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
The perimeter of a triangle = a + b + c.
where
a = first side
b = second side
c = third side
.
We are told P = 110.
.
To solve word problems, it usually is best to define these variables in terms of one another, which the problem tells you how to do so. For example,
.
a = a
b = 2a
c = b+30 = 2a+30
.
110 = a + b + c
Substituting for 'b' and 'c' defined in terms of 'a'.
110 = a + 2a + 2a+30
Collecting terms
110 = 5a + 30
Subtract 30 from both sides
80 = 5a
Equals are equal, so
5a = 80
Divide both sides by 5
a = 16
.
Substituting back into the formulas we set up above.
b = 2a = 2(16) = 32
c = b + 30 = 32 + 30 = 62
.
Checking our work:
a + b + c = 16 + 32 + 62 = 110
Done.
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