Question

If AC = 2x - 13 centimeters, BC = 3x + 4 centimeters, and AB = 36 centimeters, what is the length of BC?

A) 17 centimeters
B) 18 centimeters
C) 19 centimeters
D) 20 centimeters

Answer 1

To find the length of BC, we can use the equation (2x - 13) + (3x + 4) = 36. Solving this equation gives x = 9. Substituting x = 9 back into the equation BC = 3x + 4, we find that BC = 31.

Step-by-step explanation:

To find the length of BC, we can use the fact that the sum of the lengths of the two smaller segments should equal the length of the larger segment. So, we can write the equation:

(2x - 13) + (3x + 4) = 36

Combining like terms, we get:

5x - 9 = 36

Adding 9 to both sides, we have:

5x = 45

Dividing both sides by 5, we get:

x = 9

Now, we can substitute x = 9 back into one of the given segment lengths to find the length of BC:

BC = 3x + 4

BC = 3(9) + 4

BC = 27 + 4

BC = 31