Question

If B is the midpoint of AC, and AC=8x-20. Find BC
AB=3x-1
Show all work

Answer 1

`BC=26`

Explanation:

we know that

`AC=AB+BC` -----> equation A

In this problem

B is the midpoint of AC

so

`AB=BC` ------> equation B

substitute equation B in equation A

`AC=AB+AB` ------>
`AC=2AB` ------> equation C

we have

`AC=8x-20`

`AB=3x-1`

substitute the values in equation C and solve for x

`8x-20=2(3x-1)`

`8x-20=6x-2`

`8x-6x=20-2`

`2x=18`

`x=9`

Find AB

`AB=3x-1=3(9)-1=26`

Remember that

`AB=BC`

therefore

`BC=26`

Answer 2

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