A polynomial that represents the third side of a triangle is 3x + 12
For given question,
The perimeter of a triangle is given by the expression p = 5x+1.
the length of one side is x-4
and the length of the other side is x-6.
Let m represents the third side of the triangle.
We know that the perimeter of a triangle is the sum of all three sides of the triangle.
⇒ p = (x - 4) + (x - 6) + m
⇒ 5x + 1 = 2x - 10 + m
⇒ 5x - 2x + 1 + 11 = m
⇒ m = 3x + 12
This is an expression of the third side of a triangle.
Therefore, a polynomial that represents the third side of a triangle is 3x + 12
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