c = 2x + 3. The third side of the triangle is 2x + 3.
The key to solve this problem is using the perimeter of a triangle equation which is P = a + b + c, where a, b, and c are the sides of the triangle.
We know that the perimeter P = 3x² + 7x, let's suppose a = 6x - 7, b = 3x² - x + 4, and c is the unknow.
Clearing c from the equation:
c = P - (a + b)
c = 3x² + 7x - (6x - 7 + 3x² - x + 4)
c = 3x² + 7x - 6x + 7 - 3x² +x - 4
Grouping the equal terms:
c = 3x² - 3x² + 7x + x - 6x + 7 - 4
c = 0 + 8x - 6x + 3
c = 2x + 3