If  BD BC, BD = 5x – 26, BC = 2x + 1, and AC = 43, find AB.

AB = 24

Step-by-step explanation:

BD = 5x – 26

BC = 2x + 1

AC = 43

Using the segment addition postulate, AC = AB + BC.

We know that BD = BC, BD = 5x-26 and BC = 2x+1.  We can set up an equation to find the value of x:

5x - 26 = 2x + 1   Subtract 2x from each side

5x - 26 - 2x = 2x + 1 - 2x

3x-26 = 1  Add 26 to each side

3x-26+26 = 1+26

3x=27  Divide both sides by 3

3x/3 = 27/3

x = 9

This means that BC = 2x + 1 = 2(9) + 1 = 18 + 1 = 19.

We know that AC = AB + BC; using our given information as well as the value of BC we just found, we have

43 = AB + 19  Subtract 19 from each side

43 - 19 = AB + 19 - 19

24 = AB

step-by-step explanation:

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