Final answer:
To find AB, we first solve the equation 4x - 20 = 2x + 4 to find x, then subtract the value of BC (2x + 4) from AC (73). The solution shows that segment AB is 45 units in length.
Step-by-step explanation:
The question is regarding solving for a segment length in a geometric figure, given the lengths of other segments expressed in variable terms. We are given that segment BD ≃ BC, with BD being expressed as 4x – 20 and BC as 2x + 4. Since these segments are congruent, their lengths are equal, and we can set up the equation 4x - 20 = 2x + 4 to find the value of x. Solving for x, we get:
4x - 2x = 20 + 4
2x = 24
x = 12
Assuming that segments BD, BC, and AC are parts of a larger segment or triangle and AC represents the entire length of segment AC, then segment AB can be found by subtracting segment BC from AC. Hence, AB = AC - BC. With BC being equal to 2x + 4 and AC being 73:
AB = 73 - (2 × 12 + 4)
AB = 73 - (24 + 4)
AB = 73 - 28
AB = 45
Therefore, the length of segment AB is 45 units.