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
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
[tex]AB+BC=AC[/tex]
Substitute AC = 48, AB = 2x+2, and BC = 3x+6 in the above equation.
[tex](2x+2)+(3x+6)=48[/tex]
On combining like terms we get
[tex](2x+3x)+(2+6)=48[/tex]
[tex]5x+8=48[/tex]
Subtract 8 from both sides.
[tex]5x=48-8[/tex]
[tex]5x=40[/tex]
Divide 5 from both sides.
[tex]x=8[/tex]
The value of x is 8.
We need to find the value of BC.
[tex]BC=3x+6\Rightarrow 3(8)+6=30[/tex]
Therefore the value of BC is 30.
