Respuesta :

QueenOfLife

Answer:

AB is 24

Step-by-step explanation:

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

We know that BD=BC, BD=5x-26 and BC=2x+1. So 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

The value of AB= 24

Given :

BD is congruent to BC. BD=BC

BD = 5x – 26, BC = 2x + 1, and AC = 43

The diagram is attached below

Explanation :

From the diagram , AC=AB+BC

To find out , we need to find  BC first . For that we have to find out x

WE know that BD=BC, using that we solve for x

[tex]5x-26=2x+1\\Subtract \; 2x\\3x-26=1\\Add \; 26\\3x=27\\x=9[/tex]

Now we plug in 9 for x  and find out BC

[tex]BC=2x+1\\BC=2(9)+1\\BC=19[/tex]

We know AC= 43

[tex]AC=AB+BC\\43=AB+19\\Subtract \; 19\\\\AB=24[/tex]

Learn more :

brainly.com/question/24410700

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