Respuesta :

Louli
first we know that:
AB+BC=AC
now , since B is the midpoint of AC, this means that AB=BC
therefore,
AB+BC=AC can also be written as
AB+AB=AC
3x-1+3x-1=8x-20
6x-2=8x-20
-2+20=8x-6x
18=2x
x=9

therefore:
AB=3(9)-1=27-1=26
AC=8(9)-20=52
BC=AB=26
calculista

Answer:

[tex]BC=26[/tex]

Step-by-step explanation:

we know that

[tex]AC=AB+BC[/tex] -----> equation A

In this problem

B is the midpoint of AC

so

[tex]AB=BC[/tex] ------> equation B

substitute equation B in equation A

[tex]AC=AB+AB[/tex] ------> [tex]AC=2AB[/tex] ------> equation C

we have

[tex]AC=8x-20[/tex]

[tex]AB=3x-1[/tex]

substitute the values in equation C and solve for x

[tex]8x-20=2(3x-1)[/tex]

[tex]8x-20=6x-2[/tex]

[tex]8x-6x=20-2[/tex]

[tex]2x=18[/tex]

[tex]x=9[/tex]

Find AB

[tex]AB=3x-1=3(9)-1=26[/tex]

Remember that

[tex]AB=BC[/tex]

therefore

[tex]BC=26[/tex]

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