SOLUTION: 1. A triangle has a side lenght of 3x + 2, 2x + 1 and 4x - 1. The perimeter is 11x - 2. Find the lengths of the sides of the triangle.

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: 1. A triangle has a side lenght of 3x + 2, 2x + 1 and 4x - 1. The perimeter is 11x - 2. Find the lengths of the sides of the triangle.      Log On

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Question 989264: 1. A triangle has a side lenght of 3x + 2, 2x + 1 and 4x - 1. The perimeter is 11x - 2. Find the lengths of the sides of the triangle.
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The perimeter is the sum of the 3 sides.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

recall: the perimeter of triangle is P=a%2Bb%2Bc
if a triangle has a side lenght of a=3x+%2B+2, b=2x+%2B+1 and c=4x+-+1, and if the perimeter is P=11x+-+2, we have
11x+-+2=%283x+%2B+2%29%2B%282x+%2B+1%29%2B%284x+-+1%29......solve for x
11x+-+2=3x+%2B+2%2B2x+%2B+1%2B4x+-+1
11x+-+2=9x+%2B+2
11x+-9x=2+%2B+2
2x=4
highlight%28x=2%29

now, the lengths of the sides of the triangle will be:
a=3x+%2B+2=>a=3%2A2+%2B+2=>highlight%28a=8%29
b=2x+%2B+1 =>b=2%2A2+%2B+1 =>highlight%28b=5%29
c=4x+-+1=>c=4%2A2+-+1=>highlight%28c=7%29
and the perimeter will be:P=11x+-+2=>P=11%2A2+-+2=>highlight%28P=20%29

check:
11x+-+2=%283x+%2B+2%29%2B%282x+%2B+1%29%2B%284x+-+1%29
11%2A2+-+2=%283%2A2+%2B+2%29%2B%282%2A2+%2B+1%29%2B%284%2A2+-+1%29
20=8%2B5%2B7
20=20