SOLUTION: The perimeter of the triangle is 10x^2-5x+7 and the other two sides are x-7 and 3x^2+5 and I need the find the third side with a polynomial expression. I need help!!!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The perimeter of the triangle is 10x^2-5x+7 and the other two sides are x-7 and 3x^2+5 and I need the find the third side with a polynomial expression. I need help!!!      Log On


   

Question 985773: The perimeter of the triangle is 10x^2-5x+7 and the other two sides are x-7 and 3x^2+5 and I need the find the third side with a polynomial expression. I need help!!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let A,B,C be the three side lengths

Adding the side lengths gives the perimeter of the triangle

P = A+B+C

make the proper substitutions to get

10x^2 - 5x + 7 = (x-7)+(3x^2+5) + C

now solve for C

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10x^2 - 5x + 7 = (x-7)+(3x^2+5) + C
10x^2 - 5x + 7 = x-7+3x^2+5 + C
10x^2 - 5x + 7 = 3x^2+x-2 + C
10x^2 - 5x + 7 - 3x^2-x+2 = C
C = 10x^2 - 5x + 7 - 3x^2-x+2
C = 7x^2 - 6x + 9


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The expression for the third side is 7x^2 - 6x + 9