Question

Points A, B, and C are collinear, and B lies between A and C. If AC = 48, AB = 2x+2, and BC = 3x+6, what is BC?

Answer 1

Answer:

The value of BC is 30.

Step-by-step explanation:

Given information: A, B, and C are collinear, B lies between A and C, AC = 48, AB = 2x+2, and BC = 3x+6.

If A, B, and C are collinear, B lies between A and C, then by using segment addition property, we get

$AB+BC=AC$

Substitute AC = 48, AB = 2x+2, and BC = 3x+6 in the above equation.

$(2x+2)+(3x+6)=48$

On combining like terms we get

$(2x+3x)+(2+6)=48$

$5x+8=48$

Subtract 8 from both sides.

$5x=48-8$

$5x=40$

Divide 5 from both sides.

$x=8$

The value of x is 8.

We need to find the value of BC.

$BC=3x+6\Rightarrow 3(8)+6=30$

Therefore the value of BC is 30.

Answer 2

Answer:

BC=30

Step-by-step explanation:

AC = 48

AB = 2x+2

BC=3x+6

AC= AB + BC

48 = 2x+2+3x+6

48=5x+8

5x=40

x=8

Hence

BC = 3(8)+6

BC=24+6

BC=30