Question

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

Answer 1

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

Answer 2

Answer:

$BC=26$

Step-by-step 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

$BC=26$