Final answer:
By using the given lengths AC, BC in terms of x, and the fixed length AB, we solve for x and find that the length of BC is 31 centimeters.
Step-by-step explanation:
The student is given the lengths of segments AC and BC in terms of x and the length of segment AB, and they are asked to find the length of segment BC. We can use the fact that AB = AC + BC to set up an equation where AB is given as 36 centimeters. By substituting AC = 2x - 13 centimeters and BC = 3x + 4 centimeters into the equation 36 = (2x - 13) + (3x + 4), we can solve for x. Once we have the value of x, we can find the length of BC by substituting x back into the expression for BC.
To solve the equation, we combine like terms to get 36 = 5x - 9. Adding 9 to both sides gives us 45 = 5x, and dividing by 5 gives us x = 9. Now, we substitute x back into the expression for BC: BC = 3(9) + 4, which simplifies to BC = 27 + 4, so BC = 31 centimeters.
Therefore, the length of BC is 31 centimeters.