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If segment BD LaTeX: \cong≅ segment BC , BD = 4x – 20, BC = 2x + 4, and AC = 73, find AB.

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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.

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