SOLUTION: The longest side of the triangle is thrice the length of the shortest side.The medium-sized side is 4cm less than the longest side.The perimeter of the triangle is 31cm.how long is

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Question 1062653: The longest side of the triangle is thrice the length of the shortest side.The medium-sized side is 4cm less than the longest side.The perimeter of the triangle is 31cm.how long is the longest side?
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
let a = smallest side.
let b = medium side
let c = largest side.

a + b + c = 31

c = 3a
b = c - 4 = 3a - 4

a+ b + c = 31 becomes:

a + (3a - 4) + 3a = 31

simplify and combine like terms to get:

7a - 4 = 31

add 4 to both sides to get:

7a = 35

solve for a to get a = 5

you get:

a = 5
c = 15
b = 11

a + b + c = 31

solution is:

largest side is 15 cm.

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!

The longest side of the triangle is thrice the length of the shortest side.The medium-sized side is 4cm less than the longest side.The perimeter of the triangle is 31cm.how long is the longest side?

Let longest side be L
Then shortest side =
Middle side = L - 4
We then get: =====>
6L + L = 105 ------ Multiplying by LCD, 3
7L = 105
L, or longest side =