SOLUTION: One side of a triangle is one-third the longest side. The third side is 13 feet less than the longest side. The perimeter is 85. Find all three sides.

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Question 1124892: One side of a triangle is one-third the longest side. The third side is 13 feet less than the longest side. The perimeter is 85. Find all three sides.
Found 3 solutions by solver91311, MathLover1, MathTherapy:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!

Let represent "One side". Then the longest side is and the third side is .

The perimeter of a triangle is given by the sum of the measures of the three sides, hence:

Solve for then calculate and

John

My calculator said it, I believe it, that settles it

Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!

let's sides be ,, and where is longest
if one side of a triangle is the longest side, we have
....eq.1

if the third side is feet less than the longest side, we have
.......eq.2

if the perimeter is , we have
....eq.3 .............substitute and

...solve for

now find and

->->
->->

so, your sides are: ,, and

check the perimeter:

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

One side of a triangle is one-third the longest side. The third side is 13 feet less than the longest side. The perimeter is 85. Find all three sides.

Just ONE (1) variable is needed to solve for the value of all 3 sides
Let the first side be F
Then the longest side is 3F
Third side = 3F - 13
We then get: F + 3F + 3F - 13 = 85
7F - 13 = 85
7F = 98
F, or first side =
Longest side:
Third side: